(* 1. Set up *)

field={Γ,k,l,((a[t])^(n_)),((b[t])^(n_)),α0[t],χ0[t],α0'[t],χ0'[t],α0''[t],χ0''[t],Derivative[3][α0][t],Derivative[3][χ0][t],Ψ0[t],Ψ0'[t],Ψ0''[t],Derivative[3][Ψ0][t],Derivative[4][Ψ0][t],(OverBar[Ψ0])[t],(OverBar[Ψ0])'[t],(OverBar[Ψ0])''[t],Derivative[3][(OverBar[Ψ0])][t],Derivative[4][(OverBar[Ψ0])][t],P0[t],P0'[t],P0''[t],Derivative[3][P0][t],Derivative[4][P0][t],α1[t],χ1[t],α1'[t],χ1'[t],α1''[t],χ1''[t],Derivative[3][α1][t],Derivative[3][χ1][t],Ψ1[t],Ψ1'[t],Ψ1''[t],Derivative[3][Ψ1][t],Derivative[4][Ψ1][t],(OverBar[Ψ1])[t],(OverBar[Ψ1])'[t],(OverBar[Ψ1])''[t],Derivative[3][(OverBar[Ψ1])][t],Derivative[4][(OverBar[Ψ1])][t],P1[t],P1'[t],P1''[t],Derivative[3][P1][t],Derivative[4][P1][t],P[t],P'[t],P''[t],Derivative[3][P][t],Derivative[4][P][t],(OverTilde[α])[t],(OverTilde[χ])[t]};

rep1={a'[t]->a[t]H[t],a''[t]->a[t]((H[t])^2)+a[t]H'[t],Derivative[3][a][t]->a[t]((H[t])^3)+3a[t]H[t]H'[t]+a[t]H''[t],Derivative[4][a][t]->a[t] ((H[t])^4)+6 a[t] ((H[t])^2) H'[t]+3 a[t] ((H'[t])^2)+4 a[t] H[t] H''[t]+a[t] Derivative[3][H][t],b'[t]->b[t]G[t],b''[t]->b[t]((G[t])^2)+b[t]G'[t],Derivative[3][b][t]->b[t]((G[t])^3)+3b[t]G[t]G'[t]+b[t]G''[t],Derivative[4][b][t]->b[t] ((G[t])^4)+6 b[t] ((G[t])^2) G'[t]+3 b[t] ((G'[t])^2)+4 b[t] G[t] G''[t]+b[t] Derivative[3][G][t]};

rep3={Derivative[5][H][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-120((Subscript[H, i])/((τ[t])^6))-55440Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^12)))),Derivative[5][G][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-120((Subscript[H, i])/((τ[t])^6))-55440Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^12)))),Derivative[4][H][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(24((Subscript[H, i])/((τ[t])^5))+5040Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^11)))),Derivative[4][G][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(24((Subscript[H, i])/((τ[t])^5))+5040Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^11)))),Derivative[3][H][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-6((Subscript[H, i])/((τ[t])^4))-504Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^10)))),Derivative[3][G][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-6((Subscript[H, i])/((τ[t])^4))-504Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^10)))),H''[t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(2((Subscript[H, i])/((τ[t])^3))+56Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^9)))),G''[t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(2((Subscript[H, i])/((τ[t])^3))+56Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^9)))),H'[t]-> ((-1+(Sqrt[21]))/2)(Subscript[H, i])(-((Subscript[H, i])/((τ[t])^2))-7Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^8)))),G'[t]->((-7+(Sqrt[21]))/14)((-1+(Sqrt[21]))/2)(Subscript[H, i])(-((Subscript[H, i])/((τ[t])^2))-7Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^8)))),H[t]->((Subscript[H, i])/(τ[t]))+Γ ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^7))),G[t]->((-7+(Sqrt[21]))/14)(((Subscript[H, i])/(τ[t]))+Γ ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^7)))),τ'[t]->((-1+(Sqrt[21]))/2)(Subscript[H, i]),τ''[t]->0};

rep4={Derivative[5][H0][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-120((Subscript[H, i])/((τ[t])^6))),Derivative[5][G0][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-120((Subscript[H, i])/((τ[t])^6))),Derivative[4][H0][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(24((Subscript[H, i])/((τ[t])^5))),Derivative[4][G0][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(24((Subscript[H, i])/((τ[t])^5))),Derivative[3][H0][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-6((Subscript[H, i])/((τ[t])^4))),Derivative[3][G0][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-6((Subscript[H, i])/((τ[t])^4))),H0''[t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(2((Subscript[H, i])/((τ[t])^3))),G0''[t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(2((Subscript[H, i])/((τ[t])^3))),H0'[t]-> ((-1+(Sqrt[21]))/2)(Subscript[H, i])(-((Subscript[H, i])/((τ[t])^2))),G0'[t]->((-7+(Sqrt[21]))/14)((-1+(Sqrt[21]))/2)(Subscript[H, i])(-((Subscript[H, i])/((τ[t])^2))),H0[t]->((Subscript[H, i])/(τ[t])),G0[t]->((-7+(Sqrt[21]))/14)(((Subscript[H, i])/(τ[t]))),τ'[t]->((-1+(Sqrt[21]))/2)(Subscript[H, i]),τ''[t]->0};

rep5={Derivative[5][H1][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-55440 ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^12)))),Derivative[5][G1][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^5)(-55440 ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^12)))),Derivative[4][H1][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(5040 ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^11)))),Derivative[4][G1][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^4)(25040 ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^11)))),Derivative[3][H1][t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-504 ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^10)))),Derivative[3][G1][t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^3)(-504 ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^10)))),H1''[t]-> (((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(56 ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^9)))),G1''[t]->((-7+(Sqrt[21]))/14)(((((-1+(Sqrt[21]))/2)(Subscript[H, i])))^2)(56 ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^9)))),H1'[t]-> ((-1+(Sqrt[21]))/2)(Subscript[H, i])(-7 ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^8)))),G1'[t]->((-7+(Sqrt[21]))/14)((-1+(Sqrt[21]))/2)(Subscript[H, i])(-7 ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^8)))),H1[t]-> ((Subscript[H, i])^7)((13824 (477087-97732 (Sqrt[21])))/(8575 ((τ[t])^7))),G1[t]->((-7+(Sqrt[21]))/14)( ((Subscript[H, i])^7)((20736 (200843-34423 (Sqrt[21])))/(8575 ((τ[t])^7)))),τ'[t]->((-1+(Sqrt[21]))/2)(Subscript[H, i]),τ''[t]->0};

(* Consider l=0 modes of E1Zero, E2Zero, E3Zero, E4Zero, E7Zero with (OverBar[β])=(OverBar[χ])=σ=0 : E4Zero is automatically satisfied *)

Collect[Simplify[Normal[Series[Expand[E4Zero-D[E2Zero,t]-(7 G[t]+3 H[t])E2Zero-((k^2)/((a[t])^2))E3Zero /. rep1 //. rep3],{Γ,0,1}]]],field]

(* 2. Prescription above eq.(40) *)

Ψ[t_]:=Ψ0[t]+Γ Ψ1[t];
(OverBar[Ψ])[t_]:=(OverBar[Ψ0])[t]+Γ (OverBar[Ψ1])[t];
H[t_]:=H0[t]+Γ H1[t];
G[t_]:=G0[t]+Γ G1[t];

(* 3. SUGRA Part: eqs.(41),(42),(43) *)

solsugra={Derivative[4][H0][t]->(3/2) (((1-(Sqrt[21])))^4) ((H0[t])^5),Derivative[3][H0][t]->(3/4) (((1-(Sqrt[21])))^3) ((H0[t])^4),H0''[t]->(1/2) (((1-(Sqrt[21])))^2) ((H0[t])^3),H0'[t]-> ((1-(Sqrt[21]))/2)((H0[t])^2),Derivative[4][G0][t]->(3/28) (((1-(Sqrt[21])))^4) (-7+(Sqrt[21])) ((H0[t])^5),Derivative[3][G0][t]->(3/56) (((1-(Sqrt[21])))^3) (-7+(Sqrt[21])) ((H0[t])^4),G0''[t]->(1/28) (((1-(Sqrt[21])))^2) (-7+(Sqrt[21])) ((H0[t])^3),G0'[t]->(1/28) (1-(Sqrt[21])) (-7+(Sqrt[21])) ((H0[t])^2),G0[t]->((-7+(Sqrt[21]))/14)H0[t]};

E1SUGRA=Collect[Simplify[Expand[E1Zero/. Γ->0]],field]

E2SUGRA=Simplify[Collect[Expand[E2Zero /. Γ->0],field]]

E3SUGRA=Collect[Simplify[Expand[E3Zero/. Γ->0]],field]

E7SUGRA=Collect[Simplify[Expand[E7Zero/. Γ->0]],field]

α[t_]:=((2 H'[t]Ψ[t]+(7 ((G[t])^2)-7 G[t] H[t] +7 G'[t])(OverBar[Ψ])[t]+2 H[t] Ψ'[t]+7 G[t] (OverBar[Ψ])'[t])/(7 G[t]+2 H[t]));
χ[t_]:=((2 H[t] Ψ[t]+7 G[t] (OverBar[Ψ])[t])/(7 G[t]+2 H[t]))+(((a[t])^2)/((k^2) (((7 G[t]+2 H[t]))^2))) (21 G[t] (OverBar[Ψ])[t] (-14 ((G[t])^3)+12 G[t] ((H[t])^2)+2 ((H[t])^3)-3 H[t] G'[t])+63 ((G[t])^2)H'[t]Ψ[t]+63 ((G[t])^2) H[t] (Ψ'[t]-(OverBar[Ψ])'[t]));

Simplify[Expand[Normal[Series[α[t] /. solsugra,{Γ,0,0}]]]] (* α0=eq.(41) *)

Collect[Simplify[Expand[Normal[Series[χ[t] /. solsugra,{Γ,0,0}]]]],field] (* χ0=eq.(42) *)

Collect[FullSimplify[Expand[E1SUGRA/. Γ->0]],field]

Simplify[Collect[Expand[E2SUGRA/. Γ->0],field]]

Collect[FullSimplify[Expand[ ((k^2)/((a[t])^2))(1/(3H[t]))E3SUGRA /. rep1/. Γ->0 /. solsugra]],field](* EOM for P0, eq.(43) *)

Collect[FullSimplify[Expand[-(7/(3(7+(Sqrt[21]))H[t]))E7SUGRA+((k^2)/((a[t])^2))(1/(3H[t]))E3SUGRA //. solsugra /. rep1/. Γ->0]],field]

Clear[α,χ]

(* 4. Solve α and χ, eqs.(44),(45) *)

α[t_]:=((2 H'[t]Ψ[t]+(7 ((G[t])^2)-7 G[t] H[t] +7 G'[t])(OverBar[Ψ])[t]+2 H[t] Ψ'[t]+7 G[t] (OverBar[Ψ])'[t])/(7 G[t]+2 H[t]))+Γ (OverTilde[α])[t];
χ[t_]:=((2 H[t] Ψ[t]+7 G[t] (OverBar[Ψ])[t])/(7 G[t]+2 H[t]))+(((a[t])^2)/((k^2) (((7 G[t]+2 H[t]))^2))) (21 G[t] (OverBar[Ψ])[t] (-14 ((G[t])^3)+12 G[t] ((H[t])^2)+2 ((H[t])^3)-3 H[t] G'[t])+63 ((G[t])^2)H'[t]Ψ[t]+63 ((G[t])^2) H[t] (Ψ'[t]-(OverBar[Ψ])'[t]))+Γ (OverTilde[χ])[t];

E11Γ=Collect[Simplify[D[Expand[E1Zero //. rep1],Γ] /. Γ->0],field];
E21Γ=Collect[Simplify[D[Expand[E2Zero //. rep1],Γ] /. Γ->0],field];

solα=Solve[{E11Γ==0,E21Γ==0},{(OverTilde[α])[t],(OverTilde[χ])[t]}][[1,1,2]];
solχ=Solve[{E11Γ==0,E21Γ==0},{(OverTilde[α])[t],(OverTilde[χ])[t]}][[1,2,2]];

Collect[Simplify[Expand[solα //. solsugra]],field]

Collect[Simplify[ExpandAll[solχ //. solsugra]],field]

α[t_]:=((2 H'[t]Ψ[t]+(7 ((G[t])^2)-7 G[t] H[t] +7 G'[t])(OverBar[Ψ])[t]+2 H[t] Ψ'[t]+7 G[t] (OverBar[Ψ])'[t])/(7 G[t]+2 H[t]))+Γ (((1536 (14229047+734623 (Sqrt[21])) ((H0[t])^7) Ψ0[t])/8575)+((3072 (-14799601+828991 (Sqrt[21])) ((H0[t])^7) (OverBar[Ψ0])[t])/8575)+((1536 (-2965613-1496367 (Sqrt[21])) ((H0[t])^6) )/8575)((Ψ0)'[t]- (OverBar[Ψ0])'[t])+(((k^2) )/((a[t])^2))(-((1536 (-152147+1677 (Sqrt[21])) ((H0[t])^5) )/1225)(Ψ0[t]-(OverBar[Ψ0])[t])-((3072 (497+1348 (Sqrt[21])) ((H0[t])^4) )/1225)((Ψ0)'[t]-(OverBar[Ψ0])'[t]))+(546816/245) (136+9 (Sqrt[21])) ((H0[t])^5) ((Ψ0)''[t]-(OverBar[Ψ0])''[t])-((6144 (1771+1014 (Sqrt[21])) ((H0[t])^4) )/1225)(Derivative[3][Ψ0][t]-Derivative[3][(OverBar[Ψ0])][t]));
χ[t_]:=((2 H[t] Ψ[t]+7 G[t] (OverBar[Ψ])[t])/(7 G[t]+2 H[t]))+(((a[t])^2)/((k^2) (((7 G[t]+2 H[t]))^2))) (21 G[t] (OverBar[Ψ])[t] (-14 ((G[t])^3)+12 G[t] ((H[t])^2)+2 ((H[t])^3)-3 H[t] G'[t])+63 ((G[t])^2)H'[t]Ψ[t]+63 ((G[t])^2) H[t] (Ψ'[t]-(OverBar[Ψ])'[t]))+Γ (((3072 (-573447+5902 (Sqrt[21])) ((H0[t])^6) )/8575)(Ψ0[t]-(OverBar[Ψ0])[t])+(((k^2) )/((a[t])^2))(-((3072 (497+1348 (Sqrt[21])) ((H0[t])^4) )/1225)(Ψ0[t]-(OverBar[Ψ0])[t]))+(4608/245) (861+859 (Sqrt[21])) ((H0[t])^5) ((Ψ0)'[t]-(OverBar[Ψ0])'[t])-((6144 (1771+1014 (Sqrt[21])) ((H0[t])^4) )/1225)((Ψ0)''[t]-(OverBar[Ψ0])''[t])+(((a[t])^2)/(k^2)) (-((3072 (34956397-13586977 (Sqrt[21])) ((H0[t])^8) Ψ0[t])/8575)-((3072 (26812583+1603297 (Sqrt[21])) ((H0[t])^8) (OverBar[Ψ0])[t])/8575)-((3072 (25037012-2136942 (Sqrt[21])) ((H0[t])^7) )/8575)((Ψ0)'[t]-(OverBar[Ψ0])'[t])-((3072 (628026-719166 (Sqrt[21])) ((H0[t])^6) )/8575)((Ψ0)''[t]-(OverBar[Ψ0])''[t])-((3072 (34463+217 (Sqrt[21])) ((H0[t])^5) )/1225)(Derivative[3][Ψ0][t]-Derivative[3][(OverBar[Ψ0])][t])));

(* E11: E1Zero *)

E11=Collect[FullSimplify[Normal[Series[Expand[E1Zero //. rep1 //. solsugra],{Γ,0,1}]]],field]

(* E21: E2Zero *)

E21=Collect[FullSimplify[Normal[Series[Expand[E2Zero //. rep1 //. solsugra],{Γ,0,1}]]],field]

(* E31: E3Zero *)

E31=Collect[FullSimplify[Normal[Series[Expand[E3Zero //. rep1 //. solsugra],{Γ,0,1}]]],field]

(* E71: E7Zero *)

E71=Collect[FullSimplify[Normal[Series[Expand[E7Zero//. rep1 //. solsugra ],{Γ,0,1}]]],field]

(* Confirm that other equations are satisfied *)

Collect[Simplify[Normal[Series[E4Zero-D[E2Zero,t]-(7 G[t]+3 H[t])E2Zero-((k^2)/((a[t])^2))E3Zero //. rep1  //. rep4 //. rep5,{Γ,0,1}]]],field]

Collect[FullSimplify[Expand[((245 (((-3+(Sqrt[21])))^5) (7+(Sqrt[21])) ((τ[t])^7))/(Γ 35831808 (-387871+84611 (Sqrt[21])) (Subscript[H, i]^7)))((7/((7+(Sqrt[21]))))E71-((k^2)/((a[t])^2))E31) //. rep1 //. rep4 //. rep5]-ExpandAll[ ((k^2)/((a[t])^2))(1/(3H[t]))E3SUGRA //. solsugra /. rep1/. Γ->0 //. rep4]],field]

(* 5. Scalar Perturbation, eq.(46) *)

Ψ0[t_]:=P0[t]+(OverBar[Ψ0])[t];
Ψ1[t_]:=P1[t]+(OverBar[Ψ1])[t];

E32=Collect[FullSimplify[ExpandAll[(1/(3H0[t]))(((k^2) )/((a[t])^2))E31 //. rep4 //. rep5 /. {(Subscript[H, i])->H0[t] τ[t]}]],field]

E32Γ0=E32 /. Γ->0;
E32Γ1=D[E32,Γ];
E33=Sum[FullSimplify[E32Γ0[[i]]],{i,1,Length[E32Γ0]}]+Γ Sum[FullSimplify[E32Γ1[[i]]],{i,1,Length[E32Γ1]}]

N[((3+(Sqrt[21]))/6)(2^((9-(Sqrt[21]))/10))]

(* 6. Derive eqs.(62),(68),(71) *)

(* dt=a0dη, eq.(62), (68) *)

Eη1=Collect[FullSimplify[Normal[Series[Expand[((((a0[t])^2)E33 /. Γ->0) /. {Derivative[2][P0][t]->(1/((a0[t])^2))(Derivative[2][P0][η]-ℋ0[η]Derivative[1][P0][η]),Derivative[1][P0][t]->(1/(a0[t]))Derivative[1][P0][η],P0[t]->P0[η],H0[t]->((ℋ0[η])/(a0[t])),a[t]->a0[t](1+Γ(OverBar[ a1])[η])})+(((a0[t])^2)Γ D[E33,Γ] /. {Derivative[4][P0][t]->(1/((a0[t])^4))(Derivative[4][P0][η]-6 ℋ0[η]Derivative[3][P0][η]+(5+2(Sqrt[21]))((ℋ0[η])^2)Derivative[2][P0][η]-((21+(Sqrt[21]))/2)((ℋ0[η])^3)Derivative[1][P0][η]),Derivative[3][P0][t]->(1/((a0[t])^3))(Derivative[3][P0][η]-3 ℋ0[η]Derivative[2][P0][η]+((1+(Sqrt[21]))/2)((ℋ0[η])^2)Derivative[1][P0][η]),Derivative[2][P0][t]->(1/((a0[t])^2))(Derivative[2][P0][η]-ℋ0[η]Derivative[1][P0][η]),Derivative[1][P0][t]->(1/(a0[t]))Derivative[1][P0][η],P0[t]->P0[η],H0[t]->(1/(a0[t]))ℋ0[η],P1[t]->P1[η],P1'[t]->(1/(a0[t]))P1'[η],P1''[t]->(1/((a0[t])^2))(Derivative[2][P1][η]-ℋ0[η]Derivative[1][P1][η]),a[t]->a0[t]})],{Γ,0,1}]]],{Γ,a[t],P0[η],P0'[η],P0''[η],Derivative[3][P0][η],Derivative[4][P0][η],P1[η],P1'[η],P1''[η],k,ℋ0[η]}]

(* eq.(62), (71) *)

P0[η_]:=((a0[η])^(((Sqrt[21])+1)/4))U0[η];
P1[η_]:=((a0[η])^(((Sqrt[21])+1)/4))U1[η];

EC2=Collect[FullSimplify[Normal[Series[Expand[((a0[η])^(-(((Sqrt[21])+1)/4)))Eη1 //. {a0'[η]->a0[η]ℋ0[η],a0''[η]->a0[η]((ℋ0[η])^2)+a0[η]ℋ0'[η],Derivative[3][a0][η]->a0[η]((ℋ0[η])^3)+3a0[η]ℋ0[η]ℋ0'[η]+a0[η]ℋ0''[η],Derivative[4][a0][η]->a0[η] ((ℋ0[η])^4)+6 a0[η] ((ℋ0[η])^2) (ℋ0)'[η]+3 a0[η] (((ℋ0)'[η])^2)+4 a0[η] ℋ0[η] (ℋ0)''[η]+a0[η] Derivative[3][ℋ0][η],ℋ0'''[η]->(3/4) (((3-(Sqrt[21])))^3) ((ℋ0[η])^4),ℋ0''[η]->(1/2) (((3-(Sqrt[21])))^2) ((ℋ0[η])^3),ℋ0'[η]-> ((3-(Sqrt[21]))/2)((ℋ0[η])^2)}],{Γ,0,1}]]],{Γ,a0[t],U0[η],U0'[η],U0''[η],Derivative[3][U0][η],Derivative[4][U0][η],U1[η],U1'[η],U1''[η],k,ℋ0[η]}]

(* eq.(72) *)

ℋ0[η_]:=((3+(Sqrt[21]))/6)(1/η);
(OverBar[a1])[η_]:=-((1+(Sqrt[21]))/60)((13824 (477087-97732 (Sqrt[21])))/8575)(((ℋ0[η])^6)/((a0[t])^6));

EC3=Collect[FullSimplify[Expand[(1/Γ)EC2 //. {U0''[η]->-((k^2)+(1/(4 (η^2)))) U0[η],Derivative[3][U0][η]->D[-((k^2)+(1/(4 (η^2)))) U0[η],η],Derivative[4][U0][η]->D[-((k^2)+(1/(4 (η^2)))) U0[η],{η,2}]} //. {U0[η]->c1(Sqrt[k η])BesselJ[0,k η]+c2(Sqrt[k η]) BesselY[0,k η],U0'[η]->D[c1(Sqrt[k η])BesselJ[0,k η]+c2(Sqrt[k η]) BesselY[0,k η],η],a0[t]->aE((((((Sqrt[21])-3)/2)aE HI η))^((3+(Sqrt[21]))/6))}]],{U1[η],U1'[η],U1''[η]}]

(* 7. eq.(72) *)

DSolve[ (((2^8) (Sqrt[k η]))/(3 (5^2) (7^3) (aE^6) (η^8)(((aE HI η))^(3+(Sqrt[21])))))(((((3+(Sqrt[21]))/6)))^(3+(Sqrt[21])))( (36 (49428849+10780291 (Sqrt[21]))+(602616417+131422261 (Sqrt[21])) (k^2) (η^2)-44100 (37+8 (Sqrt[21])) (k^4) (η^4)) (c1 BesselJ[0,k η]+c2 BesselY[0,k η])+ (-78 (27149229+5923661 (Sqrt[21]))k η +420 (127267+27753 (Sqrt[21])) (k^3) (η^3))(c1 BesselJ[1,k η]+c2 BesselY[1,k η]))+((k^2)+(1/(4 (η^2)))) U1[η]+U1''[η]==0,U1[η],η]

solU1=-((2^(7-(Sqrt[21]))) (3^(-(3/2)-(Sqrt[21]))) (((3+(Sqrt[21])))^(Sqrt[21])) (((aE HI η))^(-(Sqrt[21]))) (-99629224212 (Sqrt[3]) c1 π (Sqrt[η]) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-65222640324 (Sqrt[7]) c1 π (Sqrt[η]) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-676610750088 (Sqrt[3]) c2 π (Sqrt[η]) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[1+(1/2) (-11-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-442945717776 (Sqrt[7]) c2 π (Sqrt[η]) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[1+(1/2) (-11-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-39564955972 (Sqrt[3]) c1 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-25901345674 (Sqrt[7]) c1 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-229132055761 (Sqrt[3]) c2 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[1+(1/2) (-9-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-150002143817 (Sqrt[7]) c2 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[1+(1/2) (-9-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+128933700 (Sqrt[3]) c1 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+84407400 (Sqrt[7]) c1 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+617760150 (Sqrt[3]) c2 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[1+(1/2) (-7-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+404419050 (Sqrt[7]) c2 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[1+(1/2) (-7-(Sqrt[21]))] HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+69533515974 (Sqrt[3]) c1 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+45520372248 (Sqrt[7]) c1 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+402688608777 (Sqrt[3]) c2 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[(3/2)+(1/2) (-10-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+263621576829 (Sqrt[7]) c2 (k^2) π (η^(5/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] Gamma[(3/2)+(1/2) (-10-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-2120853770 (Sqrt[3]) c1 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-1388425290 (Sqrt[7]) c1 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-10161622940 (Sqrt[3]) c2 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(3/2)+(1/2) (-8-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-6652343880 (Sqrt[7]) c2 (k^4) π (η^(9/2)) (Sqrt[k η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(3/2)+(1/2) (-8-(Sqrt[21]))] HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+1235520300 c2 (k^4) (Sqrt[3 π]) (η^(9/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (15+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]+808838100 c2 (k^4) (Sqrt[7 π]) (η^(9/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (15+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]-40646491760 c2 (k^3) (Sqrt[3 π]) (η^(7/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (17+2 (Sqrt[21]))},{(1/4),(1/4)}},{{-(1/4),-(1/4),(3/4)},{(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]-26609375520 c2 (k^3) (Sqrt[7 π]) (η^(7/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (17+2 (Sqrt[21]))},{(1/4),(1/4)}},{{-(1/4),-(1/4),(3/4)},{(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]-458264111522 c2 (k^2) (Sqrt[3 π]) (η^(5/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (19+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]-300004287634 c2 (k^2) (Sqrt[7 π]) (η^(5/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (19+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]+1610754435108 c2 k (Sqrt[3 π]) (η^(3/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (21+2 (Sqrt[21]))},{(1/4),(1/4)}},{{-(1/4),-(1/4),(3/4)},{(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]+1054486307316 c2 k (Sqrt[7 π]) (η^(3/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (21+2 (Sqrt[21]))},{(1/4),(1/4)}},{{-(1/4),-(1/4),(3/4)},{(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]-1353221500176 c2 (Sqrt[3 π]) (Sqrt[η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (23+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]-885891435552 c2 (Sqrt[7 π]) (Sqrt[η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4) (23+2 (Sqrt[21]))},{(3/4),(3/4)}},{{(1/4),(1/4),(1/4)},{(3/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]+20323245880 c2 (k^3) (Sqrt[3 π]) (η^(7/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4),(1/4) (17+2 (Sqrt[21]))},{-(3/4)}},{{-(1/4),(3/4)},{-(3/4),-(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]+13304687760 c2 (k^3) (Sqrt[7 π]) (η^(7/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4),(1/4) (17+2 (Sqrt[21]))},{-(3/4)}},{{-(1/4),(3/4)},{-(3/4),-(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]-805377217554 c2 k (Sqrt[3 π]) (η^(3/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4),(1/4) (21+2 (Sqrt[21]))},{-(3/4)}},{{-(1/4),(3/4)},{-(3/4),-(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]-527243153658 c2 k (Sqrt[7 π]) (η^(3/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(1/4),(1/4) (21+2 (Sqrt[21]))},{-(3/4)}},{{-(1/4),(3/4)},{-(3/4),-(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]+617760150 c1 (k^4) (Sqrt[3 π]) (η^(9/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (15+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]+404419050 c1 (k^4) (Sqrt[7 π]) (η^(9/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (15+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]-617760150 c2 (k^4) (Sqrt[3 π]) (η^(9/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (15+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]-404419050 c2 (k^4) (Sqrt[7 π]) (η^(9/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (15+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (11+2 (Sqrt[21]))}},k η,(1/2)]-20323245880 c1 (k^3) (Sqrt[3 π]) (η^(7/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (17+2 (Sqrt[21]))},{(1/4)}},{{(3/4),(3/4)},{-(1/4),-(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]-13304687760 c1 (k^3) (Sqrt[7 π]) (η^(7/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (17+2 (Sqrt[21]))},{(1/4)}},{{(3/4),(3/4)},{-(1/4),-(1/4),(1/4) (13+2 (Sqrt[21]))}},k η,(1/2)]-229132055761 c1 (k^2) (Sqrt[3 π]) (η^(5/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (19+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]-150002143817 c1 (k^2) (Sqrt[7 π]) (η^(5/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (19+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]+229132055761 c2 (k^2) (Sqrt[3 π]) (η^(5/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (19+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]+150002143817 c2 (k^2) (Sqrt[7 π]) (η^(5/2)) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (19+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (15+2 (Sqrt[21]))}},k η,(1/2)]+805377217554 c1 k (Sqrt[3 π]) (η^(3/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (21+2 (Sqrt[21]))},{(1/4)}},{{(3/4),(3/4)},{-(1/4),-(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]+527243153658 c1 k (Sqrt[7 π]) (η^(3/2)) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (21+2 (Sqrt[21]))},{(1/4)}},{{(3/4),(3/4)},{-(1/4),-(1/4),(1/4) (17+2 (Sqrt[21]))}},k η,(1/2)]-676610750088 c1 (Sqrt[3 π]) (Sqrt[η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (23+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]-442945717776 c1 (Sqrt[7 π]) (Sqrt[η]) BesselJ[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (23+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]+676610750088 c2 (Sqrt[3 π]) (Sqrt[η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (23+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]+442945717776 c2 (Sqrt[7 π]) (Sqrt[η]) BesselY[0,k η] Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))] MeijerG[{{(3/4),(1/4) (23+2 (Sqrt[21]))},{-(1/4)}},{{(1/4),(1/4)},{-(1/4),(1/4),(1/4) (19+2 (Sqrt[21]))}},k η,(1/2)]))/(8575 (189+41 (Sqrt[21])) (aE^9) (HI^3) (η^(19/2)) Gamma[(1/2) (-7-(Sqrt[21]))] Gamma[(1/2) (-5-(Sqrt[21]))] Gamma[(1/2) (-3-(Sqrt[21]))]);

solU1simplify=-((288 (20727-4523 (Sqrt[21])))/300125)  ((c1 (HI^6))/((((((Sqrt[21])-3)/2)η aE HI))^(9+(Sqrt[21]))))(Sqrt[k η]) (2 π BesselY[0,k η] (-6 (1371162219+299210621 (Sqrt[21])) HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-(3267117844+712937461 (Sqrt[21])) (k^2) (η^2) HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+7350 (1449+316 (Sqrt[21])) (k^4) (η^4) HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+39 (147225227+32127118 (Sqrt[21])) (k^2) (η^2) HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-245 (714837+155983 (Sqrt[21])) (k^4) (η^4) HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)])+(Sqrt[π]) BesselJ[0,k η] (78 (1705246067+372115053 (Sqrt[21])) k η MeijerG[{{(1/2),5+((Sqrt[21])/2)},{0}},{{(1/2),(1/2)},{-(1/2),-(1/2),(1/2) (8+(Sqrt[21]))}},k η,(1/2)]+7350 (13881+3029 (Sqrt[21])) (k^4) (η^4) MeijerG[{{(1/2),(1/2) (7+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (5+(Sqrt[21]))}},k η,(1/2)]-1960 (1712457+373688 (Sqrt[21])) (k^3) (η^3) MeijerG[{{(1/2),(1/2) (8+(Sqrt[21]))},{0}},{{(1/2),(1/2)},{-(1/2),-(1/2),(1/2) (6+(Sqrt[21]))}},k η,(1/2)]-(37841511589+8257680071 (Sqrt[21])) (k^2) (η^2) MeijerG[{{(1/2),(1/2) (9+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (7+(Sqrt[21]))}},k η,(1/2)]-72 (1551990251+338671484 (Sqrt[21])) MeijerG[{{(1/2),(1/2) (11+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (9+(Sqrt[21]))}},k η,(1/2)])) +((288 (-852327+185993 (Sqrt[21])) (Sqrt[π]))/1500625)((c2 (HI^6))/(((((-3+(Sqrt[21]))/2)aE HI η))^(9+(Sqrt[21])))) (Sqrt[k η]) (BesselJ[0,k η] (7350 (119133+25997 (Sqrt[21]))(Sqrt[π]) (k^4) (η^4) HypergeometricPFQ[{(1/2),-(5/2)-((Sqrt[21])/2)},{1,1,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-980 (14697276+3207209 (Sqrt[21])) (Sqrt[π]) (k^4)  (η^4) HypergeometricPFQ[{(3/2),-(5/2)-((Sqrt[21])/2)},{2,2,-(3/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+(-268697011733-58634496497 (Sqrt[21]))(Sqrt[π]) (k^2)  (η^2) HypergeometricPFQ[{(1/2),-(7/2)-((Sqrt[21])/2)},{1,1,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]+39 (12108259609+2642238881 (Sqrt[21]))(Sqrt[π])(k^2) (η^2) HypergeometricPFQ[{(3/2),-(7/2)-((Sqrt[21])/2)},{2,2,-(5/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-24 (28192114587+6152023858 (Sqrt[21])) (Sqrt[π]) HypergeometricPFQ[{(1/2),-(9/2)-((Sqrt[21])/2)},{1,1,-(7/2)-((Sqrt[21])/2)},-(k^2) (η^2)]-14700 (570801+124559 (Sqrt[21])) (k^4) (η^4) MeijerG[{{(1/2) (7+(Sqrt[21]))},{(1/2),(1/2)}},{{0,0,0},{(1/2),(1/2) (5+(Sqrt[21]))}},k η,(1/2)]+1960 (140837769+30733321 (Sqrt[21])) (k^3) (η^3) MeijerG[{{(1/2) (8+(Sqrt[21]))},{0,0}},{{-(1/2),-(1/2),(1/2)},{0,(1/2) (6+(Sqrt[21]))}},k η,(1/2)]+4 (778050877142+169784621803 (Sqrt[21])) (k^2) (η^2) MeijerG[{{(1/2) (9+(Sqrt[21]))},{(1/2),(1/2)}},{{0,0,0},{(1/2),(1/2) (7+(Sqrt[21]))}},k η,(1/2)]-312 (35061208441+7650982944 (Sqrt[21])) k η MeijerG[{{5+((Sqrt[21])/2)},{0,0}},{{-(1/2),-(1/2),(1/2)},{0,(1/2) (8+(Sqrt[21]))}},k η,(1/2)]+72 (127640510767+27853443103 (Sqrt[21])) MeijerG[{{(1/2) (11+(Sqrt[21]))},{(1/2),(1/2)}},{{0,0,0},{(1/2),(1/2) (9+(Sqrt[21]))}},k η,(1/2)])+ BesselY[0,k η] (7350 (570801+124559 (Sqrt[21])) (k^4) (η^4) MeijerG[{{(1/2),(1/2) (7+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (5+(Sqrt[21]))}},k η,(1/2)]-980 (140837769+30733321 (Sqrt[21])) (k^3) (η^3) MeijerG[{{0,(1/2) (8+(Sqrt[21]))},{-1}},{{-(1/2),(1/2)},{-1,-(1/2),(1/2) (6+(Sqrt[21]))}},k η,(1/2)]-2 (778050877142+169784621803 (Sqrt[21])) (k^2) (η^2) MeijerG[{{(1/2),(1/2) (9+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (7+(Sqrt[21]))}},k η,(1/2)]+156 (35061208441+7650982944 (Sqrt[21])) k η MeijerG[{{0,5+((Sqrt[21])/2)},{-1}},{{-(1/2),(1/2)},{-1,-(1/2),(1/2) (8+(Sqrt[21]))}},k η,(1/2)]-36 (127640510767+27853443103 (Sqrt[21])) MeijerG[{{(1/2),(1/2) (11+(Sqrt[21]))},{-(1/2)}},{{0,0},{-(1/2),0,(1/2) (9+(Sqrt[21]))}},k η,(1/2)]));

FullSimplify[solU1-solU1simplify]

(* Set up : E1Zero=eq.(36) *)

E1Zero=(1/((a[t])^4))(k^4) ((1/10125)1024 Γ α[t] (6839 ((G[t])^4)-16429 ((G[t])^3) H[t]+23807 ((G[t])^2) ((H[t])^2)-25683 G[t] ((H[t])^3)+11466 ((H[t])^4)+10927 ((G[t])^2) (G'[t]-H'[t])+9254 G[t] H[t] (G'[t]-H'[t])-20181 ((H[t])^2) (G'[t]-H'[t])+15554 (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ (OverBar[Ψ])[t] (-4942 ((G[t])^5)+28007 ((G[t])^4) H[t]-61726 ((G[t])^3) ((H[t])^2)+59199 ((G[t])^2) ((H[t])^3)-20538 G[t] ((H[t])^4)+8239 ((G[t])^3) (G'[t]-H'[t])-31192 ((G[t])^2) H[t] (G'[t]-H'[t])+22953 G[t] ((H[t])^2) (G'[t]-H'[t])-7357 G[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ Ψ[t] (-1897 ((G[t])^4) H[t]-11578 ((G[t])^3) ((H[t])^2)+37919 ((G[t])^2) ((H[t])^3)-33516 G[t] ((H[t])^4)+9072 ((H[t])^5)-19166 ((G[t])^2) H[t] (G'[t]-H'[t])+21938 G[t] ((H[t])^2) (G'[t]-H'[t])-2772 ((H[t])^3) (G'[t]-H'[t])-8197 H[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ χ[t] (4942 ((G[t])^5)-26110 ((G[t])^4) H[t]+73304 ((G[t])^3) ((H[t])^2)-97118 ((G[t])^2) ((H[t])^3)+54054 G[t] ((H[t])^4)-9072 ((H[t])^5)-8239 ((G[t])^3) (G'[t]-H'[t])+50358 ((G[t])^2) H[t] (G'[t]-H'[t])-44891 G[t] ((H[t])^2) (G'[t]-H'[t])+2772 ((H[t])^3) (G'[t]-H'[t])+7357 G[t] (((G'[t]-H'[t]))^2)+8197 H[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ (-6839 ((G[t])^4)+16429 ((G[t])^3) H[t]-23807 ((G[t])^2) ((H[t])^2)+25683 G[t] ((H[t])^3)-11466 ((H[t])^4)-10927 ((G[t])^2) (G'[t]-H'[t])-9254 G[t] H[t] (G'[t]-H'[t])+20181 ((H[t])^2) (G'[t]-H'[t])-15554 (((G'[t]-H'[t]))^2)) χ'[t])+(1/((a[t])^2))(k^2) ((1/10125)Γ (-21324800 ((G[t])^5) H[t]+194761728 ((G[t])^4) ((H[t])^2)-567856128 ((G[t])^3) ((H[t])^3)+762911744 ((G[t])^2) ((H[t])^4)-494678016 G[t] ((H[t])^5)+126185472 ((H[t])^6)+67988480 ((G[t])^3) H[t] G'[t]-221863936 ((G[t])^2) ((H[t])^2) G'[t]+269093888 G[t] ((H[t])^3) G'[t]-115218432 ((H[t])^4) G'[t]-15841280 G[t] H[t] G'[t] (G'[t]-H'[t])+30507008 ((H[t])^2) G'[t] (G'[t]-H'[t])+40298496 ((G[t])^4) H'[t]-201614336 ((G[t])^3) H[t] H'[t]+410281984 ((G[t])^2) ((H[t])^2) H'[t]-406246400 G[t] ((H[t])^3) H'[t]+157280256 ((H[t])^4) H'[t]+19367936 G[t] H[t] (G'[t]-H'[t]) H'[t]-61601792 ((H[t])^2) (G'[t]-H'[t]) H'[t]+29331456 (((G'[t]-H'[t]))^2) H'[t]-27568128 ((G[t])^2) H'[t] (-G'[t]+H'[t])) Ψ'[t]+(1/10125)Γ (21324800 ((G[t])^6)-194761728 ((G[t])^5) H[t]+567856128 ((G[t])^4) ((H[t])^2)-762911744 ((G[t])^3) ((H[t])^3)+494678016 ((G[t])^2) ((H[t])^4)-126185472 G[t] ((H[t])^5)-108286976 ((G[t])^4) G'[t]+355489792 ((G[t])^3) H[t] G'[t]-457511936 ((G[t])^2) ((H[t])^2) G'[t]+252370944 G[t] ((H[t])^3) G'[t]-42061824 ((H[t])^4) G'[t]-34033664 G[t] H[t] G'[t] (G'[t]-H'[t])+31094784 ((H[t])^2) G'[t] (G'[t]-H'[t])-29331456 G'[t] (((G'[t]-H'[t]))^2)+67988480 ((G[t])^4) H'[t]-221863936 ((G[t])^3) H[t] H'[t]+269093888 ((G[t])^2) ((H[t])^2) H'[t]-115218432 G[t] ((H[t])^3) H'[t]+30507008 G[t] H[t] (G'[t]-H'[t]) H'[t]+11726848 ((G[t])^2) G'[t] (-G'[t]+H'[t])+15841280 ((G[t])^2) H'[t] (-G'[t]+H'[t])) (OverBar[Ψ])'[t]+(1/10125)Γ α[t] (-142220288 ((G[t])^6)+758008832 ((G[t])^5) H[t]-1815711744 ((G[t])^4) ((H[t])^2)+2468501504 ((G[t])^3) ((H[t])^3)-1958018048 ((G[t])^2) ((H[t])^4)+836656128 G[t] ((H[t])^5)-147216384 ((H[t])^6)+7168 ((G[t])^2) ((H[t])^2) (66486 G'[t]-65748 H'[t])-7168 G[t] ((H[t])^3) (61892 G'[t]-57308 H'[t])+64512 ((H[t])^4) (1942 G'[t]-1701 H'[t])-516096 ((G[t])^3) H[t] (239 G'[t]-289 H'[t])+14336 G[t] H[t] (12563 G'[t]-8471 H'[t]) (G'[t]-H'[t])-7168 ((H[t])^2) (12563 G'[t]-8471 H'[t]) (G'[t]-H'[t])+43997184 (((G'[t]-H'[t]))^3)+7168 ((G[t])^2) (12563 G'[t]-8471 H'[t]) (-G'[t]+H'[t])+7168 ((G[t])^4) (-4864 G'[t]+2941 H'[t])-13784064 ((G[t])^3) G''[t]+12020736 ((G[t])^2) H[t] G''[t]+17310720 G[t] ((H[t])^2) G''[t]-15547392 ((H[t])^3) G''[t]-29331456 G[t] G'[t] G''[t]+29331456 G[t] H'[t] G''[t]+29331456 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])+13784064 ((G[t])^3) H''[t]-12020736 ((G[t])^2) H[t] H''[t]-17310720 G[t] ((H[t])^2) H''[t]+15547392 ((H[t])^3) H''[t]+29331456 G[t] G'[t] H''[t]-29331456 G[t] H'[t] H''[t])+(1/10125)Γ χ'[t] (120895488 ((G[t])^6)-541922304 ((G[t])^5) H[t]+1053093888 ((G[t])^4) ((H[t])^2)-1137733632 ((G[t])^3) ((H[t])^3)+700428288 ((G[t])^2) ((H[t])^4)-215792640 G[t] ((H[t])^5)+21030912 ((H[t])^6)+143152128 ((G[t])^4) G'[t]-300131328 ((G[t])^3) H[t] G'[t]+202804224 ((G[t])^2) ((H[t])^2) G'[t]-77822976 G[t] ((H[t])^3) G'[t]+31997952 ((H[t])^4) G'[t]-130228224 G[t] H[t] G'[t] (G'[t]-H'[t])+28449792 ((H[t])^2) G'[t] (G'[t]-H'[t])-14665728 G'[t] (((G'[t]-H'[t]))^2)-129368064 ((G[t])^4) H'[t]+274326528 ((G[t])^3) H[t] H'[t]-208094208 ((G[t])^2) ((H[t])^2) H'[t]+110681088 G[t] ((H[t])^3) H'[t]-47545344 ((H[t])^4) H'[t]+71565312 G[t] H[t] (G'[t]-H'[t]) H'[t]+881664 ((H[t])^2) (G'[t]-H'[t]) H'[t]+14665728 (((G'[t]-H'[t]))^2) H'[t]-101778432 ((G[t])^2) G'[t] (-G'[t]+H'[t])+72446976 ((G[t])^2) H'[t] (-G'[t]+H'[t])+13784064 ((G[t])^3) G''[t]-12020736 ((G[t])^2) H[t] G''[t]-17310720 G[t] ((H[t])^2) G''[t]+15547392 ((H[t])^3) G''[t]+29331456 G[t] G'[t] G''[t]-29331456 G[t] H'[t] G''[t]-29331456 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])-13784064 ((G[t])^3) H''[t]+12020736 ((G[t])^2) H[t] H''[t]+17310720 G[t] ((H[t])^2) H''[t]-15547392 ((H[t])^3) H''[t]-29331456 G[t] G'[t] H''[t]+29331456 G[t] H'[t] H''[t])+Ψ[t] (2 H[t]+(1/10125)Γ (293888 ((G[t])^6) H[t]+565060608 ((G[t])^5) ((H[t])^2)-2289939456 ((G[t])^4) ((H[t])^3)+3590573056 ((G[t])^3) ((H[t])^4)-2687096832 ((G[t])^2) ((H[t])^5)+935165952 G[t] ((H[t])^6)-114057216 ((H[t])^7)+564178944 ((G[t])^4) H[t] G'[t]-9189376 H[t] ((G'[t])^3)+7168 ((G[t])^2) ((H[t])^3) (182280 G'[t]-19921 H'[t])-150528 ((G[t])^3) ((H[t])^2) (9962 G'[t]-4231 H'[t])-21324800 ((G[t])^5) H'[t]-288820224 ((G[t])^4) H[t] H'[t]+179214336 ((H[t])^5) H'[t]+67988480 ((G[t])^3) G'[t] H'[t]-15841280 G[t] ((G'[t])^2) H'[t]+58075136 H[t] ((G'[t])^2) H'[t]-67988480 ((G[t])^3) ((H'[t])^2)+31682560 G[t] G'[t] ((H'[t])^2)-88582144 H[t] G'[t] ((H'[t])^2)-15841280 G[t] ((H'[t])^3)+39696384 H[t] ((H'[t])^3)-43008 G[t] ((H[t])^4) (8631 G'[t]+8444 H'[t])+43008 ((H[t])^3) (937 ((G'[t])^2)-3912 G'[t] H'[t]+2975 ((H'[t])^2))+7168 ((G[t])^2) H[t] (19083 ((G'[t])^2)-65272 G'[t] H'[t]+46189 ((H'[t])^2))-7168 G[t] ((H[t])^2) (24705 ((G'[t])^2)-79259 G'[t] H'[t]+54554 ((H'[t])^2))+80596992 ((G[t])^3) H[t] G''[t]-214222848 ((G[t])^2) ((H[t])^2) G''[t]+186654720 G[t] ((H[t])^3) G''[t]-53028864 ((H[t])^4) G''[t]+27568128 G[t] H[t] (G'[t]-H'[t]) G''[t]-27568128 ((H[t])^2) (G'[t]-H'[t]) G''[t]+20149248 ((G[t])^4) H''[t]-147409920 ((G[t])^3) H[t] H''[t]+308431872 ((G[t])^2) ((H[t])^2) H''[t]-255230976 G[t] ((H[t])^3) H''[t]+74059776 ((H[t])^4) H''[t]-25804800 G[t] H[t] (G'[t]-H'[t]) H''[t]+12020736 ((H[t])^2) (G'[t]-H'[t]) H''[t]+14665728 (((G'[t]-H'[t]))^2) H''[t]-13784064 ((G[t])^2) (-G'[t]+H'[t]) H''[t]))+(OverBar[Ψ])[t] (7 G[t]+(1/10125)Γ (141485568 ((G[t])^7)-1380872192 ((G[t])^6) H[t]+4380601344 ((G[t])^5) ((H[t])^2)-6586696704 ((G[t])^4) ((H[t])^3)+5162920448 ((G[t])^3) ((H[t])^4)-2032708608 ((G[t])^2) ((H[t])^5)+315270144 G[t] ((H[t])^6)-568436736 ((G[t])^5) G'[t]+1628583936 ((G[t])^4) H[t] G'[t]-1497925632 ((G[t])^3) ((H[t])^2) G'[t]+257660928 ((G[t])^2) ((H[t])^3) G'[t]+306302976 G[t] ((H[t])^4) G'[t]-126185472 ((H[t])^5) G'[t]-135399936 ((G[t])^3) ((G'[t])^2)+216201216 ((G[t])^2) H[t] ((G'[t])^2)-196019712 G[t] ((H[t])^2) ((G'[t])^2)+115218432 ((H[t])^3) ((G'[t])^2)-33632256 G[t] ((G'[t])^3)-30507008 H[t] G'[t] (((G'[t]-H'[t]))^2)+522948608 ((G[t])^5) H'[t]-1554330624 ((G[t])^4) H[t] H'[t]+1659614208 ((G[t])^3) ((H[t])^2) H'[t]-748030976 ((G[t])^2) ((H[t])^3) H'[t]+119798784 G[t] ((H[t])^4) H'[t]+204574720 ((G[t])^3) G'[t] H'[t]-214065152 ((G[t])^2) H[t] G'[t] H'[t]+124708864 G[t] ((H[t])^2) G'[t] H'[t]-115218432 ((H[t])^3) G'[t] H'[t]+116738048 G[t] ((G'[t])^2) H'[t]-69174784 ((G[t])^3) ((H'[t])^2)-2136064 ((G[t])^2) H[t] ((H'[t])^2)+71310848 G[t] ((H[t])^2) ((H'[t])^2)-132579328 G[t] G'[t] ((H'[t])^2)+49473536 G[t] ((H'[t])^3)-86962176 ((G[t])^4) G''[t]+269015040 ((G[t])^3) H[t] G''[t]-298174464 ((G[t])^2) ((H[t])^2) G''[t]+137152512 G[t] ((H[t])^3) G''[t]-21030912 ((H[t])^4) G''[t]-3526656 G[t] H[t] (G'[t]-H'[t]) G''[t]+15547392 ((H[t])^2) (G'[t]-H'[t]) G''[t]-14665728 (((G'[t]-H'[t]))^2) G''[t]+12020736 ((G[t])^2) (-G'[t]+H'[t]) G''[t]+66812928 ((G[t])^4) H''[t]-202202112 ((G[t])^3) H[t] H''[t]+203965440 ((G[t])^2) ((H[t])^2) H''[t]-68576256 G[t] ((H[t])^3) H''[t]+1763328 G[t] H[t] (G'[t]-H'[t]) H''[t]+1763328 ((G[t])^2) (-G'[t]+H'[t]) H''[t]))+χ[t] (((-70875 G[t]-20250 H[t])/10125)+(1/10125)Γ (-141485568 ((G[t])^7)+1380578304 ((G[t])^6) H[t]-4945661952 ((G[t])^5) ((H[t])^2)+8876636160 ((G[t])^4) ((H[t])^3)-8753493504 ((G[t])^3) ((H[t])^4)+4719805440 ((G[t])^2) ((H[t])^5)-1250436096 G[t] ((H[t])^6)+114057216 ((H[t])^7)+135399936 ((G[t])^3) ((G'[t])^2)+33632256 G[t] ((G'[t])^3)+39696384 H[t] ((G'[t])^3)-43008 ((G[t])^2) ((H[t])^3) (36371 G'[t]-20713 H'[t])+387072 ((G[t])^3) ((H[t])^2) (7744 G'[t]-5933 H'[t])-473088 ((G[t])^4) H[t] (4635 G'[t]-3896 H'[t])+387072 ((H[t])^5) (326 G'[t]-463 H'[t])-272563200 ((G[t])^3) G'[t] H'[t]-100896768 G[t] ((G'[t])^2) H'[t]-119089152 H[t] ((G'[t])^2) H'[t]+137163264 ((G[t])^3) ((H'[t])^2)+100896768 G[t] G'[t] ((H'[t])^2)+119089152 H[t] G'[t] ((H'[t])^2)-33632256 G[t] ((H'[t])^3)-39696384 H[t] ((H'[t])^3)+21504 G[t] ((H[t])^4) (3018 G'[t]+11317 H'[t])-7168 ((G[t])^5) (-79302 G'[t]+69981 H'[t])+7168 ((G[t])^2) H[t] (-49245 ((G'[t])^2)+95136 G'[t] H'[t]-45891 ((H'[t])^2))-43008 ((H[t])^3) (3616 ((G'[t])^2)-6591 G'[t] H'[t]+2975 ((H'[t])^2))+10752 G[t] ((H[t])^2) (34701 ((G'[t])^2)-64438 G'[t] H'[t]+29737 ((H'[t])^2))+86962176 ((G[t])^4) G''[t]-349612032 ((G[t])^3) H[t] G''[t]+512397312 ((G[t])^2) ((H[t])^2) G''[t]-323807232 G[t] ((H[t])^3) G''[t]+74059776 ((H[t])^4) G''[t]-24041472 G[t] H[t] (G'[t]-H'[t]) G''[t]+12020736 ((H[t])^2) (G'[t]-H'[t]) G''[t]+14665728 (((G'[t]-H'[t]))^2) G''[t]-12020736 ((G[t])^2) (-G'[t]+H'[t]) G''[t]-86962176 ((G[t])^4) H''[t]+349612032 ((G[t])^3) H[t] H''[t]-512397312 ((G[t])^2) ((H[t])^2) H''[t]+323807232 G[t] ((H[t])^3) H''[t]-74059776 ((H[t])^4) H''[t]+24041472 G[t] H[t] (G'[t]-H'[t]) H''[t]-12020736 ((H[t])^2) (G'[t]-H'[t]) H''[t]-14665728 (((G'[t]-H'[t]))^2) H''[t]+12020736 ((G[t])^2) (-G'[t]+H'[t]) H''[t]))+(1/10125)Γ (20149248 ((G[t])^5)-86962176 ((G[t])^4) H[t]+161021952 ((G[t])^3) ((H[t])^2)-162785280 ((G[t])^2) ((H[t])^3)+89607168 G[t] ((H[t])^4)-21030912 ((H[t])^5)+13784064 ((G[t])^3) G'[t]-12020736 ((G[t])^2) H[t] G'[t]-17310720 G[t] ((H[t])^2) G'[t]+15547392 ((H[t])^3) G'[t]+14665728 G[t] ((G'[t])^2)-14665728 H[t] (((G'[t]-H'[t]))^2)-13784064 ((G[t])^3) H'[t]+12020736 ((G[t])^2) H[t] H'[t]+17310720 G[t] ((H[t])^2) H'[t]-15547392 ((H[t])^3) H'[t]-29331456 G[t] G'[t] H'[t]+14665728 G[t] ((H'[t])^2)) χ''[t]+(1/10125)Γ (20149248 ((G[t])^4) H[t]-66812928 ((G[t])^3) ((H[t])^2)+94209024 ((G[t])^2) ((H[t])^3)-68576256 G[t] ((H[t])^4)+21030912 ((H[t])^5)+13784064 ((G[t])^2) H[t] G'[t]+1763328 G[t] ((H[t])^2) G'[t]-15547392 ((H[t])^3) G'[t]+14665728 H[t] (((G'[t]-H'[t]))^2)-13784064 ((G[t])^2) H[t] H'[t]-1763328 G[t] ((H[t])^2) H'[t]+15547392 ((H[t])^3) H'[t]) Ψ''[t]+(1/10125)Γ (-20149248 ((G[t])^5)+66812928 ((G[t])^4) H[t]-94209024 ((G[t])^3) ((H[t])^2)+68576256 ((G[t])^2) ((H[t])^3)-21030912 G[t] ((H[t])^4)-13784064 ((G[t])^3) G'[t]-1763328 ((G[t])^2) H[t] G'[t]+15547392 G[t] ((H[t])^2) G'[t]-14665728 G[t] ((G'[t])^2)+13784064 ((G[t])^3) H'[t]+1763328 ((G[t])^2) H[t] H'[t]-15547392 G[t] ((H[t])^2) H'[t]+29331456 G[t] G'[t] H'[t]-14665728 G[t] ((H'[t])^2)) (OverBar[Ψ])''[t])+(OverBar[Ψ])[t] (((7 (6750 G[t] G'[t]+3375 H[t] G'[t]))/1125)+(1/1125)7 Γ (-86817792 G[t] ((H[t])^6) G'[t]+9004032 ((H[t])^7) G'[t]+3696640 G[t] ((G'[t])^4)-1601536 H[t] ((G'[t])^4)+1024 G[t] ((G'[t])^3) (6949 ((H[t])^2)-9466 H'[t])-4694016 G[t] ((H[t])^4) G'[t] H'[t]+3407872 H[t] ((G'[t])^3) H'[t]-2299904 G[t] G'[t] ((H'[t])^3)+204800 H[t] G'[t] ((H'[t])^3)-2002944 ((H[t])^6) G''[t]+1396736 G[t] G'[t] ((G''[t])^2)-1396736 H[t] G'[t] ((G''[t])^2)+3584 ((G[t])^6) (13159 H[t] G'[t]+1874 G''[t])+3072 ((H[t])^4) (-1460 H'[t] G''[t]+G'[t] (2608 G''[t]-1389 H''[t]))-1024 ((H[t])^2) (G'[t]-H'[t]) (-2087 H'[t] G''[t]+G'[t] (1528 G''[t]-805 H''[t]))-1024 G[t] ((H[t])^3) G'[t] (20451 G''[t]-15140 H''[t])+26624 G[t] H[t] G'[t] H'[t] (299 G''[t]-43 H''[t])-1396736 G[t] G'[t] G''[t] H''[t]+1396736 H[t] G'[t] G''[t] H''[t]-698368 (((G'[t]-H'[t]))^2) (-H'[t] G''[t]+G'[t] H''[t])+1024 ((G[t])^4) (461070 ((H[t])^3) G'[t]+44328 ((H[t])^2) G''[t]-6657 H'[t] G''[t]+G'[t] (11983 G''[t]-4685 H''[t])+H[t] (-132170 ((G'[t])^2)+107265 G'[t] H'[t]-4044 Derivative[3][G][t]))+3072 ((H[t])^5) (496 ((G'[t])^2)-2211 G'[t] H'[t]-326 Derivative[3][G][t])+7168 G[t] ((H[t])^2) G'[t] (1063 ((H'[t])^2)-115 Derivative[3][G][t])-1396736 G[t] G'[t] H'[t] Derivative[3][G][t]+1396736 H[t] G'[t] H'[t] Derivative[3][G][t]-2048 H[t] ((G'[t])^2) (982 ((H'[t])^2)+341 Derivative[3][G][t])+2048 G[t] ((G'[t])^2) (14029 ((H[t])^4)-7195 ((H[t])^2) H'[t]+4051 ((H'[t])^2)+H[t] (-2905 G''[t]+559 H''[t])+341 Derivative[3][G][t])-698368 H[t] H'[t] (-2 ((G''[t])^2)+2 G''[t] H''[t]+H'[t] Derivative[3][G][t])-1024 ((G[t])^5) (226335 ((H[t])^2) G'[t]+26434 H[t] G''[t]-937 (42 ((G'[t])^2)-36 G'[t] H'[t]+Derivative[3][G][t]))-1024 ((G[t])^3) (494558 ((H[t])^4) G'[t]-14596 ((G'[t])^3)+26628 ((G'[t])^2) H'[t]+38014 ((H[t])^3) G''[t]+H[t] (-11393 H'[t] G''[t]+G'[t] (28769 G''[t]-16176 H''[t]))-48 ((H[t])^2) (3694 ((G'[t])^2)-2733 G'[t] H'[t]+156 Derivative[3][G][t])-G'[t] (12032 ((H'[t])^2)+641 Derivative[3][G][t])+641 (-((G''[t])^2)+G''[t] H''[t]+H'[t] Derivative[3][G][t]))-512 ((H[t])^3) (5311 ((G'[t])^3)-13678 ((G'[t])^2) H'[t]+3 G'[t] (2789 ((H'[t])^2)-482 Derivative[3][G][t])+1446 (-((G''[t])^2)+G''[t] H''[t]+H'[t] Derivative[3][G][t]))+1024 G[t] (1488 ((H[t])^5) G''[t]+6839 ((H[t])^3) H'[t] G''[t]-1964 H[t] ((H'[t])^2) G''[t]+4167 ((H[t])^4) Derivative[3][G][t]-805 ((H[t])^2) (((G''[t])^2)-G''[t] H''[t]-H'[t] Derivative[3][G][t])+682 H'[t] (-2 ((G''[t])^2)+2 G''[t] H''[t]+H'[t] Derivative[3][G][t]))+512 ((G[t])^2) (579513 ((H[t])^5) G'[t]+28058 ((H[t])^4) G''[t]+2 ((H[t])^2) (-7195 H'[t] G''[t]+G'[t] (29413 G''[t]-22464 H''[t]))+2 (G'[t]-H'[t]) (-4051 H'[t] G''[t]+3 G'[t] (2446 G''[t]-641 H''[t]))-4 ((H[t])^3) (57021 ((G'[t])^2)-34434 G'[t] H'[t]+3785 Derivative[3][G][t])+H[t] (-37779 ((G'[t])^3)+68358 ((G'[t])^2) H'[t]-G'[t] (30579 ((H'[t])^2)+1118 Derivative[3][G][t])+1118 (-((G''[t])^2)+G''[t] H''[t]+H'[t] Derivative[3][G][t])))))+Ψ[t] (((23625 G[t] H'[t]+6750 H[t] H'[t])/1125)+(1/1125)Γ (47161856 ((G[t])^7) H'[t]+441197568 G[t] ((H[t])^6) H'[t]-23998464 ((H[t])^7) H'[t]+53329920 G[t] ((H[t])^4) G'[t] H'[t]-11210752 G[t] ((G'[t])^3) H'[t]-3454976 H[t] ((G'[t])^3) H'[t]-29919232 H[t] G'[t] ((H'[t])^3)-3584 G[t] (25101 ((H[t])^2)+3928 G'[t]) ((H'[t])^3)+1433600 G[t] ((H'[t])^4)+13232128 H[t] ((H'[t])^4)+21504 G[t] ((H[t])^3) H'[t] (5556 G''[t]-8345 H''[t])+21030912 ((H[t])^6) H''[t]+9777152 G[t] H'[t] G''[t] H''[t]-9777152 H[t] H'[t] G''[t] H''[t]-9777152 G[t] H'[t] ((H''[t])^2)+9777152 H[t] H'[t] ((H''[t])^2)-14336 G[t] H[t] G'[t] H'[t] (805 G''[t]+1159 H''[t])-7168 ((G[t])^6) (75445 H[t] H'[t]+5622 H''[t])+4888576 (((G'[t]-H'[t]))^2) (-H'[t] G''[t]+G'[t] H''[t])+7168 ((H[t])^2) (G'[t]-H'[t]) (3 H'[t] (723 G''[t]-1646 H''[t])+1405 G'[t] H''[t])-21504 ((H[t])^4) (H'[t] (1630 G''[t]-3331 H''[t])+1460 G'[t] H''[t])+7168 ((G[t])^5) (276642 ((H[t])^2) H'[t]-26434 G'[t] H'[t]+21453 ((H'[t])^2)+21453 H[t] H''[t]-937 Derivative[3][H][t])-7010304 ((H[t])^5) (12 G'[t] H'[t]-18 ((H'[t])^2)-Derivative[3][H][t])+9777152 G[t] G'[t] H'[t] Derivative[3][H][t]-9777152 H[t] G'[t] H'[t] Derivative[3][H][t]+14336 H[t] ((H'[t])^2) (1405 ((G'[t])^2)+341 Derivative[3][H][t])-7168 G[t] ((H'[t])^2) (33165 ((H[t])^4)-20517 ((H[t])^2) G'[t]-3328 ((G'[t])^2)+H[t] (-1610 G''[t]+1010 H''[t])+682 Derivative[3][H][t])-3584 G[t] ((H[t])^2) H'[t] (15933 ((G'[t])^2)+1610 Derivative[3][H][t])+4888576 H[t] G'[t] (2 G''[t] H''[t]-2 ((H''[t])^2)+G'[t] Derivative[3][H][t])+21504 ((H[t])^3) (2438 ((G'[t])^2) H'[t]+3402 ((H'[t])^3)+241 H''[t] (-G''[t]+H''[t])+241 H'[t] Derivative[3][H][t]-G'[t] (5840 ((H'[t])^2)+241 Derivative[3][H][t]))-7168 ((G[t])^4) (494558 ((H[t])^3) H'[t]+4 H'[t] (1011 G''[t]-2515 H''[t])+32796 ((H[t])^2) H''[t]+6657 G'[t] H''[t]-12 H[t] (7388 G'[t] H'[t]-5466 ((H'[t])^2)+337 Derivative[3][H][t]))+3584 ((G[t])^3) (965855 ((H[t])^4) H'[t]-12593 ((G'[t])^2) H'[t]-10193 ((H'[t])^3)+45912 ((H[t])^3) H''[t]-1282 G''[t] H''[t]+1282 ((H''[t])^2)+H[t] (H'[t] (29952 G''[t]-50338 H''[t])+22786 G'[t] H''[t])+2 G'[t] (11393 ((H'[t])^2)-641 Derivative[3][H][t])+1282 H'[t] Derivative[3][H][t]-12 ((H[t])^2) (19007 G'[t] H'[t]-11478 ((H'[t])^2)+1248 Derivative[3][H][t]))-7168 G[t] (6633 ((H[t])^5) H''[t]-6839 ((H[t])^3) G'[t] H''[t]-3328 H[t] ((G'[t])^2) H''[t]+4167 ((H[t])^4) Derivative[3][H][t]+682 G'[t] (2 G''[t] H''[t]-2 ((H''[t])^2)+G'[t] Derivative[3][H][t])-805 ((H[t])^2) (G''[t] H''[t]-((H''[t])^2)+G'[t] Derivative[3][H][t]))-7168 ((G[t])^2) (254349 ((H[t])^5) H'[t]+2292 ((H[t])^4) H''[t]+(G'[t]-H'[t]) (H'[t] (559 G''[t]-3928 H''[t])+4733 G'[t] H''[t])+((H[t])^2) (H'[t] (22710 G''[t]-30151 H''[t])+7195 G'[t] H''[t])+((H[t])^3) (-56116 G'[t] H'[t]+9168 ((H'[t])^2)-7570 Derivative[3][H][t])+H[t] (-6949 ((G'[t])^2) H'[t]-7441 ((H'[t])^3)+559 H''[t] (-G''[t]+H''[t])+G'[t] (14390 ((H'[t])^2)-559 Derivative[3][H][t])+559 H'[t] Derivative[3][H][t]))))+(Ψ'[t] -α[t] )(((23625 G[t] H[t]+6750 ((H[t])^2))/1125)+(1/1125)Γ (47161856 ((G[t])^7) H[t]+441197568 G[t] ((H[t])^7)-23998464 ((H[t])^8)-11210752 G[t] H[t] ((G'[t])^3)-3454976 ((H[t])^2) ((G'[t])^3)+21504 G[t] ((H[t])^5) (2480 G'[t]-15477 H'[t])-84123648 ((H[t])^6) (G'[t]-2 H'[t])+71565312 G[t] H[t] ((G'[t])^2) H'[t]+40284160 ((H[t])^2) ((G'[t])^2) H'[t]+9777152 (((G'[t]-H'[t]))^3) H'[t]-70389760 G[t] H[t] G'[t] ((H'[t])^2)-89757696 ((H[t])^2) G'[t] ((H'[t])^2)+10035200 G[t] H[t] ((H'[t])^3)+52928512 ((H[t])^2) ((H'[t])^3)-7168 ((G[t])^6) (75445 ((H[t])^2)+11244 H'[t])+43008 ((H[t])^4) (1219 ((G'[t])^2)-4380 G'[t] H'[t]+3402 ((H'[t])^2))-3584 G[t] ((H[t])^3) (15933 ((G'[t])^2)-68390 G'[t] H'[t]+58569 ((H'[t])^2))-14336 ((G[t])^4) (247279 ((H[t])^4)+(6657 G'[t]-6016 H'[t]) H'[t]+((H[t])^2) (-44328 G'[t]+65592 H'[t])+2022 H[t] (G''[t]-4 H''[t]))-7168 ((G[t])^2) (254349 ((H[t])^6)+((H[t])^4) (-56116 G'[t]+13752 H'[t])+((H[t])^2) (-6949 ((G'[t])^2)+28780 G'[t] H'[t]-22323 ((H'[t])^2))+2 H'[t] (4733 ((G'[t])^2)-8102 G'[t] H'[t]+3369 ((H'[t])^2))+559 H[t] (G'[t] (G''[t]-4 H''[t])-3 H'[t] (G''[t]-2 H''[t]))+22710 ((H[t])^3) (G''[t]-2 H''[t]))+7168 ((G[t])^5) (276642 ((H[t])^3)+H[t] (-26434 G'[t]+64359 H'[t])-2811 H''[t])-7010304 ((H[t])^5) (5 G''[t]-8 H''[t])+29869056 G[t] ((H[t])^4) (4 G''[t]-7 H''[t])-4888576 G[t] (G'[t]-H'[t]) (H'[t] (4 G''[t]-7 H''[t])+3 G'[t] H''[t])-5770240 G[t] ((H[t])^2) (G'[t] (2 G''[t]-5 H''[t])+H'[t] (-4 G''[t]+7 H''[t]))-4888576 H[t] (G'[t]-H'[t]) (G'[t] (G''[t]-4 H''[t])+H'[t] (-5 G''[t]+8 H''[t]))+5182464 ((H[t])^3) (3 G'[t] (G''[t]-2 H''[t])+H'[t] (-5 G''[t]+8 H''[t]))+3584 ((G[t])^3) (965855 ((H[t])^5)+((H[t])^3) (-228084 G'[t]+229560 H'[t])+H[t] (-12593 ((G'[t])^2)+68358 G'[t] H'[t]-50965 ((H'[t])^2))+14976 ((H[t])^2) (2 G''[t]-5 H''[t])-1282 (H'[t] (2 G''[t]-5 H''[t])+3 G'[t] H''[t]))))+((OverBar[Ψ])'[t] -α[t] )(((7 (6750 ((G[t])^2)+3375 G[t] H[t]))/1125)+(1/1125)7 Γ (47161856 ((G[t])^7) H[t]-86817792 ((G[t])^2) ((H[t])^6)+9004032 G[t] ((H[t])^7)+14786560 ((G[t])^2) ((G'[t])^3)-11210752 G[t] H[t] ((G'[t])^3)-1024 ((G[t])^6) (226335 ((H[t])^2)-3748 (14 G'[t]-9 H'[t]))+4096 ((G[t])^2) ((H[t])^4) (14029 G'[t]-1146 H'[t])+9216 G[t] ((H[t])^5) (496 G'[t]-737 H'[t])-29079552 ((G[t])^2) ((G'[t])^2) H'[t]+17039360 G[t] H[t] ((G'[t])^2) H'[t]+16592896 ((G[t])^2) G'[t] ((H'[t])^2)-6033408 G[t] H[t] G'[t] ((H'[t])^2)-2299904 ((G[t])^2) ((H'[t])^3)+204800 G[t] H[t] ((H'[t])^3)+1024 ((G[t])^2) ((H[t])^2) (20847 ((G'[t])^2)-28780 G'[t] H'[t]+7441 ((H'[t])^2))-512 G[t] ((H[t])^3) (26555 ((G'[t])^2)-41034 G'[t] H'[t]+8367 ((H'[t])^2))+1024 ((G[t])^5) (461070 ((H[t])^3)+H[t] (-185038 G'[t]+107265 H'[t])+937 (8 G''[t]-5 H''[t]))-2048 ((G[t])^4) (247279 ((H[t])^4)-14596 ((G'[t])^2)-72 ((H[t])^2) (1847 G'[t]-911 H'[t])+19971 G'[t] H'[t]-6016 ((H'[t])^2)+2022 H[t] (7 G''[t]-4 H''[t]))-7751680 ((G[t])^2) ((H[t])^3) (5 G''[t]-2 H''[t])+4267008 G[t] ((H[t])^4) (4 G''[t]-H''[t])+698368 G[t] (G'[t]-H'[t]) (G'[t] (8 G''[t]-5 H''[t])+H'[t] (-4 G''[t]+H''[t]))-824320 G[t] ((H[t])^2) (G'[t] (6 G''[t]-3 H''[t])+H'[t] (-4 G''[t]+H''[t]))-572416 ((G[t])^2) H[t] (G'[t] (7 G''[t]-4 H''[t])+H'[t] (-5 G''[t]+2 H''[t]))+512 ((G[t])^3) (579513 ((H[t])^5)-4 ((H[t])^3) (95035 G'[t]-34434 H'[t])+H[t] (-88151 ((G'[t])^2)+113930 G'[t] H'[t]-30579 ((H'[t])^2))+44928 ((H[t])^2) (2 G''[t]-H''[t])+1282 (G'[t] (8 G''[t]-5 H''[t])+3 H'[t] (-2 G''[t]+H''[t])))-1024 (3912 ((H[t])^6) G'[t]+1364 G'[t] (((G'[t]-H'[t]))^3)+((H[t])^4) (-7314 ((G'[t])^2)+8760 G'[t] H'[t])+2 ((H[t])^2) G'[t] (723 ((G'[t])^2)-2810 G'[t] H'[t]+2087 ((H'[t])^2))+2934 ((H[t])^5) G''[t]+682 H[t] (G'[t]-H'[t]) (-3 H'[t] G''[t]+G'[t] (7 G''[t]-4 H''[t]))+723 ((H[t])^3) (3 H'[t] G''[t]+G'[t] (-5 G''[t]+2 H''[t])))))-(1/1125)7168 Γ (5622 ((G[t])^6) H[t]+((G[t])^4) H[t] (32796 ((H[t])^2)+6657 G'[t]-18148 H'[t])-3 ((G[t])^5) (7151 ((H[t])^2)-937 H'[t])+((G[t])^2) H[t] (2292 ((H[t])^4)+4733 ((G'[t])^2)+((H[t])^2) (7195 G'[t]-30151 H'[t])-9779 G'[t] H'[t]+5046 ((H'[t])^2)-559 H[t] (G''[t]-H''[t]))+((G[t])^3) (-22956 ((H[t])^4)+1923 (G'[t]-H'[t]) H'[t]+((H[t])^2) (-11393 G'[t]+32657 H'[t])+641 H[t] (G''[t]-H''[t]))+G[t] (6633 ((H[t])^6)+2046 (((G'[t]-H'[t]))^2) H'[t]+((H[t])^4) (-6839 G'[t]+20868 H'[t])+((H[t])^2) (-3328 ((G'[t])^2)+1513 G'[t] H'[t]+1815 ((H'[t])^2))-805 ((H[t])^3) (G''[t]-H''[t])+1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t]))-H[t] (2934 ((H[t])^6)+682 (((G'[t]-H'[t]))^2) (G'[t]+2 H'[t])+((H[t])^4) (-4380 G'[t]+8037 H'[t])+((H[t])^2) (1405 ((G'[t])^2)-6343 G'[t] H'[t]+4938 ((H'[t])^2))-723 ((H[t])^3) (G''[t]-H''[t])+1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t]))) (Ψ''[t]-α'[t])+(1/1125)7168 Γ (6559 ((G[t])^7)-26434 ((G[t])^6) H[t]-3 H[t] G'[t] (978 ((H[t])^4)-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2))+((G[t])^5) (44328 ((H[t])^2)+10109 G'[t]-6657 H'[t])+((G[t])^4) (-38014 ((H[t])^3)+H[t] (-24725 G'[t]+11393 H'[t])+641 (G''[t]-H''[t]))+((G[t])^3) (14029 ((H[t])^4)+7338 ((G'[t])^2)+((H[t])^2) (29413 G'[t]-7195 H'[t])-11389 G'[t] H'[t]+4051 ((H'[t])^2)-559 H[t] (G''[t]-H''[t]))+((G[t])^2) (1488 ((H[t])^5)-7 ((H[t])^3) (4003 G'[t]-977 H'[t])+H[t] (-6369 ((G'[t])^2)+8333 G'[t] H'[t]-1964 ((H'[t])^2))-805 ((H[t])^2) (G''[t]-H''[t])+1364 (G'[t]-H'[t]) (G''[t]-H''[t]))+G[t] (-1956 ((H[t])^6)+6 ((H[t])^4) (2693 G'[t]-730 H'[t])+682 (((G'[t]-H'[t]))^2) (2 G'[t]+H'[t])+((H[t])^2) (-3138 ((G'[t])^2)+5225 G'[t] H'[t]-2087 ((H'[t])^2))+723 ((H[t])^3) (G''[t]-H''[t])-1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])))( (OverBar[Ψ])''[t]-α'[t])+(1/1125)7168 Γ (G[t]-H[t]) (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) (H[t] (α''[t]-Derivative[3][Ψ][t])+G[t] (-α''[t]+Derivative[3][(OverBar[Ψ])][t]));

(* E2Zero=eq.(37) *)

E2Zero=(1/((a[t])^2))(k^2) (-(1/10125)512 Γ (13678 ((G[t])^4)-32858 ((G[t])^3) H[t]+47614 ((G[t])^2) ((H[t])^2)-51366 G[t] ((H[t])^3)+22932 ((H[t])^4)+21854 ((G[t])^2) G'[t]+18508 G[t] H[t] G'[t]-40362 ((H[t])^2) G'[t]+31108 G'[t] (G'[t]-H'[t])-21854 ((G[t])^2) H'[t]-18508 G[t] H[t] H'[t]+40362 ((H[t])^2) H'[t]-31108 (G'[t]-H'[t]) H'[t]) α'[t]-(1/10125)512 Γ (-3794 ((G[t])^4) H[t]-23156 ((G[t])^3) ((H[t])^2)+75838 ((G[t])^2) ((H[t])^3)-67032 G[t] ((H[t])^4)+18144 ((H[t])^5)-38332 ((G[t])^2) H[t] G'[t]+43876 G[t] ((H[t])^2) G'[t]-5544 ((H[t])^3) G'[t]-16394 H[t] G'[t] (G'[t]-H'[t])+38332 ((G[t])^2) H[t] H'[t]-43876 G[t] ((H[t])^2) H'[t]+5544 ((H[t])^3) H'[t]+16394 H[t] (G'[t]-H'[t]) H'[t]) Ψ'[t]-(1/10125)512 Γ (-9884 ((G[t])^5)+56014 ((G[t])^4) H[t]-123452 ((G[t])^3) ((H[t])^2)+118398 ((G[t])^2) ((H[t])^3)-41076 G[t] ((H[t])^4)+16478 ((G[t])^3) G'[t]-62384 ((G[t])^2) H[t] G'[t]+45906 G[t] ((H[t])^2) G'[t]-16478 ((G[t])^3) H'[t]+62384 ((G[t])^2) H[t] H'[t]-45906 G[t] ((H[t])^2) H'[t]+14714 G[t] G'[t] (-G'[t]+H'[t])-14714 G[t] H'[t] (-G'[t]+H'[t])) (OverBar[Ψ])'[t]-(1/10125)512 Γ α[t] (105630 ((G[t])^5)-295904 ((G[t])^4) H[t]+512764 ((G[t])^3) ((H[t])^2)-601412 ((G[t])^2) ((H[t])^3)+319998 G[t] ((H[t])^4)-41076 ((H[t])^5)-14 G[t] ((H[t])^2) (21114 G'[t]-16909 H'[t])+14 ((G[t])^3) (13658 G'[t]-12097 H'[t])+14 ((G[t])^2) H[t] (7846 G'[t]-8085 H'[t])+14 H[t] (271 G'[t]-4715 H'[t]) (G'[t]-H'[t])-14 G[t] (19727 G'[t]-15283 H'[t]) (-G'[t]+H'[t])+14 ((H[t])^3) (-390 G'[t]+3273 H'[t])+21854 ((G[t])^2) G''[t]+18508 G[t] H[t] G''[t]+62216 (G'[t]-H'[t]) G''[t]-40362 ((H[t])^2) (G''[t]-H''[t])-21854 ((G[t])^2) H''[t]-18508 G[t] H[t] H''[t]-62216 (G'[t]-H'[t]) H''[t])-(1/10125)512 Γ χ'[t] (-95746 ((G[t])^5)+243684 ((G[t])^4) H[t]-366156 ((G[t])^3) ((H[t])^2)+407176 ((G[t])^2) ((H[t])^3)-211890 G[t] ((H[t])^4)+22932 ((H[t])^5)-207690 ((G[t])^3) G'[t]-9128 ((G[t])^2) H[t] G'[t]+205814 G[t] ((H[t])^2) G'[t]+11004 ((H[t])^3) G'[t]+12600 H[t] G'[t] (G'[t]-H'[t])+185836 ((G[t])^3) H'[t]+12474 ((G[t])^2) H[t] H'[t]-146944 G[t] ((H[t])^2) H'[t]-51366 ((H[t])^3) H'[t]+49616 H[t] (G'[t]-H'[t]) H'[t]+261464 G[t] G'[t] (-G'[t]+H'[t])-199248 G[t] H'[t] (-G'[t]+H'[t])-21854 ((G[t])^2) G''[t]-18508 G[t] H[t] G''[t]-62216 (G'[t]-H'[t]) G''[t]+40362 ((H[t])^2) (G''[t]-H''[t])+21854 ((G[t])^2) H''[t]+18508 G[t] H[t] H''[t]+62216 (G'[t]-H'[t]) H''[t])-(1/10125)512 Γ Ψ[t] (-318038 ((G[t])^4) ((H[t])^2)+921508 ((G[t])^3) ((H[t])^3)-971054 ((G[t])^2) ((H[t])^4)+449736 G[t] ((H[t])^5)-82152 ((H[t])^6)-306656 ((G[t])^3) H[t] G'[t]+21000 ((H[t])^4) G'[t]+14 ((G[t])^2) ((H[t])^2) (26572 G'[t]-15283 H'[t])-3794 ((G[t])^4) H'[t]+245168 ((G[t])^3) H[t] H'[t]+2688 ((H[t])^4) H'[t]-38332 ((G[t])^2) G'[t] H'[t]-16394 G'[t] (G'[t]-H'[t]) H'[t]+38332 ((G[t])^2) ((H'[t])^2)+16394 (G'[t]-H'[t]) ((H'[t])^2)-14 G[t] ((H[t])^3) (6168 G'[t]+2150 H'[t])+14 ((H[t])^2) (817 ((G'[t])^2)+312 G'[t] H'[t]-1129 ((H'[t])^2))-56 G[t] H[t] (2839 ((G'[t])^2)-5876 G'[t] H'[t]+3037 ((H'[t])^2))-38332 ((G[t])^2) H[t] G''[t]+43876 G[t] ((H[t])^2) G''[t]-5544 ((H[t])^3) G''[t]-32788 H[t] (G'[t]-H'[t]) G''[t]+38332 ((G[t])^2) H[t] H''[t]-43876 G[t] ((H[t])^2) H''[t]+5544 ((H[t])^3) H''[t]+32788 H[t] (G'[t]-H'[t]) H''[t])-(1/10125)512 Γ (OverBar[Ψ])[t] (-105630 ((G[t])^6)+613942 ((G[t])^5) H[t]-1434272 ((G[t])^4) ((H[t])^2)+1572466 ((G[t])^3) ((H[t])^3)-769734 ((G[t])^2) ((H[t])^4)+123228 G[t] ((H[t])^5)+105560 ((G[t])^4) G'[t]-425838 ((G[t])^3) H[t] G'[t]+258496 ((G[t])^2) ((H[t])^2) G'[t]+102858 G[t] ((H[t])^3) G'[t]-41076 ((H[t])^4) G'[t]-100716 ((G[t])^2) ((G'[t])^2)-77616 G[t] H[t] ((G'[t])^2)+45906 ((H[t])^2) G'[t] (G'[t]-H'[t])-14714 G'[t] (((G'[t]-H'[t]))^2)-98966 ((G[t])^4) H'[t]+402990 ((G[t])^3) H[t] H'[t]-273658 ((G[t])^2) ((H[t])^2) H'[t]-30366 G[t] ((H[t])^3) H'[t]+188482 ((G[t])^2) G'[t] H'[t]+122276 G[t] H[t] G'[t] H'[t]-87766 ((G[t])^2) ((H'[t])^2)-44660 G[t] H[t] ((H'[t])^2)+16478 ((G[t])^3) G''[t]-62384 ((G[t])^2) H[t] G''[t]+45906 G[t] ((H[t])^2) G''[t]+29428 G[t] (-G'[t]+H'[t]) G''[t]-16478 ((G[t])^3) H''[t]+62384 ((G[t])^2) H[t] H''[t]-45906 G[t] ((H[t])^2) H''[t]-29428 G[t] (-G'[t]+H'[t]) H''[t])-(1/10125)512 Γ χ[t] (105630 ((G[t])^6)-613942 ((G[t])^5) H[t]+1752310 ((G[t])^4) ((H[t])^2)-2493974 ((G[t])^3) ((H[t])^3)+1740788 ((G[t])^2) ((H[t])^4)-572964 G[t] ((H[t])^5)+82152 ((H[t])^6)+100716 ((G[t])^2) ((G'[t])^2)+14 ((G[t])^3) H[t] (52321 G'[t]-46297 H'[t])-14 G[t] ((H[t])^3) (1179 G'[t]-4319 H'[t])-2268 ((G[t])^2) ((H[t])^2) (278 G'[t]-215 H'[t])+84 ((H[t])^4) (239 G'[t]-32 H'[t])-150150 ((G[t])^2) G'[t] H'[t]+49434 ((G[t])^2) ((H'[t])^2)+14 ((G[t])^4) (-7540 G'[t]+7340 H'[t])-28 G[t] H[t] (-8450 ((G'[t])^2)+16119 G'[t] H'[t]-7669 ((H'[t])^2))+14 (G'[t]-H'[t]) (1051 ((G'[t])^2)+120 G'[t] H'[t]-1171 ((H'[t])^2))+14 ((H[t])^2) (-4096 ((G'[t])^2)+2967 G'[t] H'[t]+1129 ((H'[t])^2))-16478 ((G[t])^3) G''[t]+100716 ((G[t])^2) H[t] G''[t]-89782 G[t] ((H[t])^2) G''[t]+5544 ((H[t])^3) G''[t]+32788 H[t] (G'[t]-H'[t]) G''[t]-29428 G[t] (-G'[t]+H'[t]) G''[t]+16478 ((G[t])^3) H''[t]-100716 ((G[t])^2) H[t] H''[t]+89782 G[t] ((H[t])^2) H''[t]-5544 ((H[t])^3) H''[t]-32788 H[t] (G'[t]-H'[t]) H''[t]+29428 G[t] (-G'[t]+H'[t]) H''[t])-(1/10125)512 Γ (-13678 ((G[t])^4)+32858 ((G[t])^3) H[t]-47614 ((G[t])^2) ((H[t])^2)+51366 G[t] ((H[t])^3)-22932 ((H[t])^4)-21854 ((G[t])^2) G'[t]-18508 G[t] H[t] G'[t]+40362 ((H[t])^2) G'[t]-31108 G'[t] (G'[t]-H'[t])+21854 ((G[t])^2) H'[t]+18508 G[t] H[t] H'[t]-40362 ((H[t])^2) H'[t]+31108 (G'[t]-H'[t]) H'[t]) χ''[t])+(OverBar[Ψ])[t] (-((7 (3375 ((G[t])^2)-3375 G[t] H[t]+3375 G'[t]))/3375)-(1/3375)7 Γ (20992 ((G[t])^8)-74237440 ((G[t])^7) H[t]+100758528 ((G[t])^2) ((H[t])^6)-5999616 G[t] ((H[t])^7)+9004032 ((H[t])^6) G'[t]-34949632 ((G[t])^2) ((G'[t])^3)+2052096 G[t] H[t] ((G'[t])^3)-1601536 ((G'[t])^4)+1536 ((G[t])^2) ((H[t])^4) (132665 G'[t]-26474 H'[t])-512 ((G'[t])^3) (5311 ((H[t])^2)-8020 H'[t])-9216 G[t] ((H[t])^5) (10555 G'[t]-3586 H'[t])-5790720 ((H[t])^4) G'[t] H'[t]+83247104 ((G[t])^2) ((G'[t])^2) H'[t]+9658368 G[t] H[t] ((G'[t])^2) H'[t]+15316992 ((G[t])^2) ((H'[t])^3)+12617728 G[t] H[t] ((H'[t])^3)+903168 G'[t] ((H'[t])^3)+512 ((G[t])^6) (688572 ((H[t])^2)-144257 G'[t]+125558 H'[t])-656384 ((G[t])^2) ((G''[t])^2)-83968 G[t] H[t] ((G''[t])^2)-1396736 G'[t] ((G''[t])^2)-1024 G[t] ((H[t])^2) (H'[t] (3283 G''[t]-7230 H''[t])+2 G'[t] (2337 G''[t]-766 H''[t]))-1024 ((G[t])^5) (678898 ((H[t])^3)+H[t] (-175277 G'[t]+177248 H'[t])+1874 (9 G''[t]-5 H''[t]))+10240 ((G[t])^2) ((H[t])^3) (4864 G''[t]-3189 H''[t])-6144 G[t] ((H[t])^4) (1871 G''[t]-1630 H''[t])+3072 ((H[t])^3) G'[t] (2608 G''[t]-1063 H''[t])+2048 H[t] G'[t] H'[t] (2169 G''[t]-41 H''[t])+656384 ((G[t])^2) G''[t] H''[t]+83968 G[t] H[t] G''[t] H''[t]+1396736 G'[t] G''[t] H''[t]+1024 ((G[t])^2) H[t] (G'[t] (15884 G''[t]-8501 H''[t])-4 H'[t] (1501 G''[t]+205 H''[t]))-2048 G[t] (G'[t]-H'[t]) (G'[t] (7420 G''[t]-4051 H''[t])+H'[t] (-6097 G''[t]+3410 H''[t]))+512 ((G[t])^4) (1403009 ((H[t])^4)-156175 ((G'[t])^2)-4 ((H[t])^2) (49391 G'[t]-95498 H'[t])+220822 G'[t] H'[t]-74017 ((H'[t])^2)+4 H[t] (27026 G''[t]-15535 H''[t])-1874 Derivative[3][G][t])-1536 ((H[t])^2) G'[t] (2307 ((H'[t])^2)-482 Derivative[3][G][t])+2048 ((G'[t])^2) (744 ((H[t])^4)+3058 ((H[t])^2) H'[t]-1664 ((H'[t])^2)+H[t] (-764 G''[t]+41 H''[t])-341 Derivative[3][G][t])+656384 ((G[t])^2) H'[t] Derivative[3][G][t]+83968 G[t] H[t] H'[t] Derivative[3][G][t]+1396736 G'[t] H'[t] Derivative[3][G][t]-2048 G[t] H[t] G'[t] (11879 ((H'[t])^2)+41 Derivative[3][G][t])-512 ((G[t])^2) G'[t] (124247 ((H'[t])^2)+1282 Derivative[3][G][t])+512 G[t] ((H[t])^3) (96385 ((G'[t])^2)-129084 G'[t] H'[t]+62979 ((H'[t])^2)+6378 Derivative[3][G][t])-512 ((G[t])^2) ((H[t])^2) (180553 ((G'[t])^2)-185560 G'[t] H'[t]+49935 ((H'[t])^2)+8762 Derivative[3][G][t])-512 ((G[t])^3) (773907 ((H[t])^5)+12 ((H[t])^3) (19527 G'[t]+11515 H'[t])+4 G'[t] (9517 G''[t]-5079 H''[t])+52 ((H[t])^2) (2794 G''[t]-1685 H''[t])+10 H'[t] (-2929 G''[t]+1282 H''[t])-H[t] (237367 ((G'[t])^2)-265988 G'[t] H'[t]+60973 ((H'[t])^2)+6214 Derivative[3][G][t]))-1024 (1956 ((H[t])^5) G''[t]+5358 ((H[t])^3) H'[t] G''[t]+2810 H[t] ((H'[t])^2) G''[t]+978 ((H[t])^4) Derivative[3][G][t]-723 ((H[t])^2) (((G''[t])^2)-G''[t] H''[t]-H'[t] Derivative[3][G][t])+682 H'[t] (-2 ((G''[t])^2)+2 G''[t] H''[t]+H'[t] Derivative[3][G][t]))))+Ψ[t] (-2 H'[t]-(1/3375)2 Γ (-27012608 ((G[t])^6) H'[t]+248242176 ((G[t])^5) H[t] H'[t]-11999232 ((H[t])^6) H'[t]-3584 ((G[t])^4) (202080 ((H[t])^2)-20171 G'[t]) H'[t]-45566976 ((H[t])^4) G'[t] H'[t]-4171776 ((G'[t])^3) H'[t]+3584 (2171 ((G[t])^2)-4875 G[t] H[t]+10206 ((H[t])^2)-4856 G'[t]) ((H'[t])^3)+6616064 ((H'[t])^4)+3584 ((G[t])^3) H'[t] (275512 ((H[t])^3)-48347 H[t] G'[t]+3107 G''[t]-10701 H''[t])+7168 H[t] G'[t] H'[t] (723 G''[t]-3533 H''[t])-10752 ((H[t])^3) H'[t] (1304 G''[t]-3331 H''[t])-4888576 H'[t] G''[t] H''[t]+4888576 H'[t] ((H''[t])^2)-3584 ((H'[t])^2) (16127 ((G[t])^4)-33371 ((G[t])^3) H[t]-17604 ((H[t])^4)+18243 ((H[t])^2) G'[t]-4174 ((G'[t])^2)+((G[t])^2) (14397 ((H[t])^2)+4901 G'[t])+G[t] (20451 ((H[t])^3)-8140 H[t] G'[t]-82 G''[t]-4610 H''[t])+6 H[t] (241 G''[t]-823 H''[t])-682 Derivative[3][H][t])-4888576 G'[t] H'[t] Derivative[3][H][t]+10752 ((H[t])^2) H'[t] (2679 ((G'[t])^2)+241 Derivative[3][H][t])-3584 ((G[t])^2) H'[t] (187503 ((H[t])^4)-37107 ((H[t])^2) G'[t]-2730 ((G'[t])^2)+H[t] (8762 G''[t]-15027 H''[t])+641 Derivative[3][H][t])+3584 G[t] H'[t] (55692 ((H[t])^5)+3783 ((H[t])^3) G'[t]+9 ((H[t])^2) (1063 G''[t]-1591 H''[t])-2 G'[t] (41 G''[t]+5333 H''[t])-H[t] (3265 ((G'[t])^2)+82 Derivative[3][H][t]))+3584 (6559 ((G[t])^5) H''[t]+2934 ((H[t])^5) H''[t]-5358 ((H[t])^3) G'[t] H''[t]+2128 H[t] ((G'[t])^2) H''[t]+978 ((H[t])^4) Derivative[3][H][t]+((G[t])^4) (-18938 H[t] H''[t]+937 Derivative[3][H][t])+((G[t])^3) (21346 ((H[t])^2) H''[t]+8235 G'[t] H''[t]-3107 H[t] Derivative[3][H][t])+682 G'[t] (2 G''[t] H''[t]-2 ((H''[t])^2)+G'[t] Derivative[3][H][t])-723 ((H[t])^2) (G''[t] H''[t]-((H''[t])^2)+G'[t] Derivative[3][H][t])+((G[t])^2) (-9180 ((H[t])^3) H''[t]-6824 H[t] G'[t] H''[t]+4381 ((H[t])^2) Derivative[3][H][t]+641 (G''[t] H''[t]-((H''[t])^2)+G'[t] Derivative[3][H][t]))+G[t] (-2721 ((H[t])^4) H''[t]+3947 ((H[t])^2) G'[t] H''[t]+6056 ((G'[t])^2) H''[t]-3189 ((H[t])^3) Derivative[3][H][t]+82 H[t] (G''[t] H''[t]-((H''[t])^2)+G'[t] Derivative[3][H][t])))))+((OverBar[Ψ])'[t] -α[t])(-7 G[t]-(1/3375)7 Γ (20992 ((G[t])^7)-43428864 ((G[t])^6) H[t]+9004032 G[t] ((H[t])^6)-15400960 G[t] ((G'[t])^3)+1024 ((G[t])^5) (167094 ((H[t])^2)-937 (53 G'[t]-32 H'[t]))+28911616 G[t] ((G'[t])^2) H'[t]-14413824 G[t] G'[t] ((H'[t])^2)+903168 G[t] ((H'[t])^3)-39936 G[t] ((H[t])^4) (36 G'[t]+145 H'[t])-512 G[t] ((H[t])^2) (17879 ((G'[t])^2)-28020 G'[t] H'[t]+6921 ((H'[t])^2))-1024 ((G[t])^4) (261952 ((H[t])^3)+H[t] (-128571 G'[t]+66431 H'[t])+937 (7 G''[t]-4 H''[t]))+512 ((G[t])^3) (401913 ((H[t])^4)-60209 ((G'[t])^2)-26 ((H[t])^2) (10079 G'[t]-3915 H'[t])+78504 G'[t] H'[t]-20859 ((H'[t])^2)+18642 H[t] (2 G''[t]-H''[t]))+3265536 G[t] ((H[t])^3) (4 G''[t]-H''[t])-83968 G[t] H[t] (G'[t] (6 G''[t]-3 H''[t])+H'[t] (-4 G''[t]+H''[t]))-1024 (3912 ((H[t])^5) G'[t]+6 ((H[t])^3) G'[t] (-1545 G'[t]+1786 H'[t])+4 H[t] G'[t] (723 ((G'[t])^2)-2128 G'[t] H'[t]+1405 ((H'[t])^2))+2934 ((H[t])^4) G''[t]+682 (G'[t]-H'[t]) (-3 H'[t] G''[t]+G'[t] (7 G''[t]-4 H''[t]))+723 ((H[t])^2) (3 H'[t] G''[t]+G'[t] (-5 G''[t]+2 H''[t])))-1024 ((G[t])^2) (72501 ((H[t])^5)+((H[t])^3) (-57433 G'[t]+8793 H'[t])+H[t] (-22272 ((G'[t])^2)+27542 G'[t] H'[t]-6388 ((H'[t])^2))+4381 ((H[t])^2) (5 G''[t]-2 H''[t])+641 (G'[t] (7 G''[t]-4 H''[t])+H'[t] (-5 G''[t]+2 H''[t])))))+(Ψ'[t] -α[t])(-2 H[t]+(1/3375)2 Γ (27012608 ((G[t])^6) H[t]-199600128 G[t] ((H[t])^6)+11999232 ((H[t])^7)+4171776 H[t] ((G'[t])^3)-3584 ((G[t])^4) H[t] (20171 G'[t]-54003 H'[t])+10752 ((H[t])^5) (62501 ((G[t])^2)+4238 G'[t]-7824 H'[t])-30213120 H[t] ((G'[t])^2) H'[t]+57688064 H[t] G'[t] ((H'[t])^2)-31646720 H[t] ((H'[t])^3)-3584 ((G[t])^2) H[t] (2730 ((G'[t])^2)-18549 G'[t] H'[t]+14701 ((H'[t])^2))-3584 ((H[t])^4) (275512 ((G[t])^3)+3 G[t] (1261 G'[t]-8631 H'[t])-978 (4 G''[t]-7 H''[t]))+10752 ((H[t])^3) (67360 ((G[t])^4)-2679 ((G'[t])^2)+9653 G'[t] H'[t]-7456 ((H'[t])^2)+((G[t])^2) (-12369 G'[t]+10919 H'[t])-3189 G[t] (G''[t]-2 H''[t]))+293888 G[t] H[t] (G'[t] (G''[t]-4 H''[t])-3 H'[t] (G''[t]-2 H''[t]))-11135488 ((G[t])^3) H[t] (G''[t]-4 H''[t])-3584 (13118 ((G[t])^5) H'[t]+2 ((G[t])^3) (8235 G'[t]-7594 H'[t]) H'[t]+8 G[t] H'[t] (1514 ((G'[t])^2)-2687 G'[t] H'[t]+1173 ((H'[t])^2))+2811 ((G[t])^4) H''[t]+682 (G'[t]-H'[t]) (H'[t] (4 G''[t]-7 H''[t])+3 G'[t] H''[t])+641 ((G[t])^2) (H'[t] (2 G''[t]-5 H''[t])+3 G'[t] H''[t]))-3584 ((H[t])^2) (69264 ((G[t])^5)+((G[t])^3) (-48347 G'[t]+76063 H'[t])+G[t] (-3265 ((G'[t])^2)+16034 G'[t] H'[t]-14379 ((H'[t])^2))-4381 ((G[t])^2) (2 G''[t]-5 H''[t])+723 (G'[t] (2 G''[t]-5 H''[t])+H'[t] (-4 G''[t]+7 H''[t])))))-(1/3375)7168 Γ (6559 ((G[t])^5) H[t]+2934 ((H[t])^6)+((G[t])^3) H[t] (21346 ((H[t])^2)+8235 G'[t]-16915 H'[t])+2046 (((G'[t]-H'[t]))^2) H'[t]+((G[t])^4) (-18938 ((H[t])^2)+2811 H'[t])+((H[t])^4) (-5358 G'[t]+9015 H'[t])+((H[t])^2) (2128 ((G'[t])^2)-7789 G'[t] H'[t]+5661 ((H'[t])^2))+G[t] H[t] (-2721 ((H[t])^4)+6056 ((G'[t])^2)+((H[t])^2) (3947 G'[t]-14319 H'[t])-10502 G'[t] H'[t]+4446 ((H'[t])^2)+82 H[t] (G''[t]-H''[t]))+((G[t])^2) (-9180 ((H[t])^4)-8 ((H[t])^2) (853 G'[t]-2426 H'[t])+1923 (G'[t]-H'[t]) H'[t]+641 H[t] (G''[t]-H''[t]))-723 ((H[t])^3) (G''[t]-H''[t])+1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])) (Ψ''[t]-α'[t])+(1/3375)7168 Γ (7496 ((G[t])^6)-22982 ((G[t])^5) H[t]+3 G'[t] (978 ((H[t])^4)-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2))+((G[t])^4) (28834 ((H[t])^2)+11687 G'[t]-8235 H'[t])+((G[t])^3) (-16750 ((H[t])^3)-8 H[t] (2088 G'[t]-853 H'[t])+641 (G''[t]-H''[t]))+((G[t])^2) (1446 ((H[t])^4)+8661 ((G'[t])^2)+((H[t])^2) (16285 G'[t]-3947 H'[t])-14035 G'[t] H'[t]+5374 ((H'[t])^2)+82 H[t] (G''[t]-H''[t]))+G[t] (1956 ((H[t])^5)-6 ((H[t])^3) (2367 G'[t]-893 H'[t])+2 H[t] (846 ((G'[t])^2)-2251 G'[t] H'[t]+1405 ((H'[t])^2))-723 ((H[t])^2) (G''[t]-H''[t])+1364 (G'[t]-H'[t]) (G''[t]-H''[t])))( (OverBar[Ψ])''[t]-α'[t])+(1/3375)7168 Γ (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) (H[t] (α''[t]-Derivative[3][Ψ][t])+G[t] (-α''[t]+Derivative[3][(OverBar[Ψ])][t]));

(* E3Zero=eq.(38) *)

E3Zero=(1/((a[t])^2))(k^2) (-(1/10125)512 Γ α[t] (-1897 ((G[t])^4)-11578 ((G[t])^3) H[t]+37919 ((G[t])^2) ((H[t])^2)-33516 G[t] ((H[t])^3)+9072 ((H[t])^4)-19166 ((G[t])^2) (G'[t]-H'[t])+21938 G[t] H[t] (G'[t]-H'[t])-2772 ((H[t])^2) (G'[t]-H'[t])-8197 (((G'[t]-H'[t]))^2))-(1/10125)512 Γ (OverBar[Ψ])[t] (-13279 ((G[t])^5)+64694 ((G[t])^4) H[t]-130627 ((G[t])^3) ((H[t])^2)+120288 ((G[t])^2) ((H[t])^3)-41076 G[t] ((H[t])^4)+11578 ((G[t])^3) (G'[t]-H'[t])-55594 ((G[t])^2) H[t] (G'[t]-H'[t])+44016 G[t] ((H[t])^2) (G'[t]-H'[t])-16219 G[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ χ[t] (13279 ((G[t])^5)-79870 ((G[t])^4) H[t]+183743 ((G[t])^3) ((H[t])^2)-212996 ((G[t])^2) ((H[t])^3)+127848 G[t] ((H[t])^4)-32004 ((H[t])^5)-11578 ((G[t])^3) (G'[t]-H'[t])+48006 ((G[t])^2) H[t] (G'[t]-H'[t])-77672 G[t] ((H[t])^2) (G'[t]-H'[t])+41244 ((H[t])^3) (G'[t]-H'[t])+16219 G[t] (((G'[t]-H'[t]))^2)-24416 H[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ Ψ[t] (15176 ((G[t])^4) H[t]-53116 ((G[t])^3) ((H[t])^2)+92708 ((G[t])^2) ((H[t])^3)-86772 G[t] ((H[t])^4)+32004 ((H[t])^5)+7588 ((G[t])^2) H[t] (G'[t]-H'[t])+33656 G[t] ((H[t])^2) (G'[t]-H'[t])-41244 ((H[t])^3) (G'[t]-H'[t])+24416 H[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ (1897 ((G[t])^4)+11578 ((G[t])^3) H[t]-37919 ((G[t])^2) ((H[t])^2)+33516 G[t] ((H[t])^3)-9072 ((H[t])^4)+19166 ((G[t])^2) (G'[t]-H'[t])-21938 G[t] H[t] (G'[t]-H'[t])+2772 ((H[t])^2) (G'[t]-H'[t])+8197 (((G'[t]-H'[t]))^2)) χ'[t])+(1/10125)3584 Γ (OverBar[Ψ])'[t] (6016 ((G[t])^6)-22865 ((G[t])^5) H[t]+2 G'[t] (5868 ((H[t])^4)-4068 ((H[t])^2) (G'[t]-H'[t])-943 (((G'[t]-H'[t]))^2))+((G[t])^4) (-398 ((H[t])^2)+3422 G'[t]-2208 H'[t])+((G[t])^3) (62931 ((H[t])^3)+H[t] (-79330 G'[t]+57966 H'[t])-500 (G''[t]-H''[t]))-2 ((G[t])^2) (31644 ((H[t])^4)+((H[t])^2) (-62722 G'[t]+37311 H'[t])+4 (4394 ((G'[t])^2)-6787 G'[t] H'[t]+2393 ((H'[t])^2))+1550 H[t] (G''[t]-H''[t]))+G[t] (17604 ((H[t])^5)-72 ((H[t])^3) (851 G'[t]-262 H'[t])+3 H[t] (7965 ((G'[t])^2)-7882 G'[t] H'[t]-83 ((H'[t])^2))+3600 ((H[t])^2) (G''[t]-H''[t])-4100 (G'[t]-H'[t]) (G''[t]-H''[t])))-(1/10125)3584 Γ Ψ'[t] (6839 ((G[t])^5) H[t]+((G[t])^3) H[t] (-70721 ((H[t])^2)+47262 G'[t]-56446 H'[t])+2 ((G[t])^4) (9707 ((H[t])^2)+977 H'[t])-G[t] H[t] (62280 ((H[t])^4)-53419 ((G'[t])^2)+64974 G'[t] H'[t]-11555 ((H'[t])^2)+4 ((H[t])^2) (837 G'[t]+13010 H'[t])-4340 H[t] (G''[t]-H''[t]))+((G[t])^2) (81296 ((H[t])^4)-6388 (G'[t]-H'[t]) H'[t]+((H[t])^2) (-8022 G'[t]+45584 H'[t])+5020 H[t] (G''[t]-H''[t]))+2 (12726 ((H[t])^6)-18 ((H[t])^4) (997 G'[t]-1693 H'[t])+3677 (((G'[t]-H'[t]))^2) H'[t]+((H[t])^2) (7484 ((G'[t])^2)-32706 G'[t] H'[t]+25222 ((H'[t])^2))-4680 ((H[t])^3) (G''[t]-H''[t])+7190 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])))+(1/10125)3584 Γ α'[t] (823 ((G[t])^5)+42279 ((G[t])^4) H[t]+7848 ((H[t])^5)+((G[t])^3) (-70323 ((H[t])^2)+45554 G'[t]-40034 H'[t])-36 ((H[t])^3) (373 G'[t]-733 H'[t])+H[t] (11117 ((G'[t])^2)-40714 G'[t] H'[t]+29597 ((H'[t])^2))+((G[t])^2) (18365 ((H[t])^3)+64 H[t] (821 G'[t]-791 H'[t])+5520 (G''[t]-H''[t]))+G[t] (1008 ((H[t])^4)+76663 ((G'[t])^2)-134846 G'[t] H'[t]+58183 ((H'[t])^2)+((H[t])^2) (-84670 G'[t]+64270 H'[t])+7440 H[t] (G''[t]-H''[t]))-12960 ((H[t])^2) (G''[t]-H''[t])+18480 (G'[t]-H'[t]) (G''[t]-H''[t]))+(14336/675) Γ (2 ((G[t])^4)+38 ((G[t])^3) H[t]+33 ((H[t])^4)+((G[t])^2) (-49 ((H[t])^2)+46 (G'[t]-H'[t]))+G[t] (-24 ((H[t])^3)+62 H[t] (G'[t]-H'[t]))-108 ((H[t])^2) (G'[t]-H'[t])+77 (((G'[t]-H'[t]))^2)) α''[t]-(28672/675) Γ (14 ((G[t])^5)+266 ((G[t])^4) H[t]+((G[t])^3) (-343 ((H[t])^2)+330 G'[t]-284 H'[t])+G[t] (231 ((H[t])^4)+631 ((G'[t])^2)-1108 G'[t] H'[t]+477 ((H'[t])^2)+((H[t])^2) (-854 G'[t]+684 H'[t])+62 H[t] (G''[t]-H''[t]))-2 (6 ((H[t])^3) (2 G'[t]-11 H'[t])+H[t] (-31 ((G'[t])^2)+139 G'[t] H'[t]-108 ((H'[t])^2))+54 ((H[t])^2) (G''[t]-H''[t])-77 (G'[t]-H'[t]) (G''[t]-H''[t]))-2 ((G[t])^2) (84 ((H[t])^3)+H[t] (-274 G'[t]+266 H'[t])+23 (-G''[t]+H''[t]))) χ''[t]-(1/10125)3584 Γ H[t] (977 ((G[t])^4)-7102 ((G[t])^3) H[t]+7848 ((H[t])^4)+((G[t])^2) (19121 ((H[t])^2)-3194 (G'[t]-H'[t]))-2 G[t] (10422 ((H[t])^3)-6871 H[t] (G'[t]-H'[t]))-10548 ((H[t])^2) (G'[t]-H'[t])+3677 (((G'[t]-H'[t]))^2)) Ψ''[t]+(1/10125)3584 Γ G[t] (857 ((G[t])^4)-9382 ((G[t])^3) H[t]+5868 ((H[t])^4)+13 ((G[t])^2) (1697 ((H[t])^2)-458 (G'[t]-H'[t]))-2 G[t] (9702 ((H[t])^3)-5011 H[t] (G'[t]-H'[t]))-4068 ((H[t])^2) (G'[t]-H'[t])-943 (((G'[t]-H'[t]))^2)) (OverBar[Ψ])''[t]+χ'[t] (1+(1/3375)Γ (-6995968 ((G[t])^6)-89410048 ((G[t])^5) H[t]+4386816 ((H[t])^6)-45635072 ((G'[t])^3)-21504 ((H[t])^4) (1706 G'[t]-1501 H'[t])+87230976 ((G'[t])^2) H'[t]-37556736 G'[t] ((H'[t])^2)-4039168 ((H'[t])^3)+3584 ((G[t])^4) (12769 ((H[t])^2)-34969 G'[t]+23819 H'[t])-11038720 ((G''[t])^2)+22077440 G''[t] H''[t]-11038720 ((H''[t])^2)-107520 ((H[t])^3) (53 G''[t]+19 H''[t])+3584 ((G[t])^3) (66531 ((H[t])^3)+H[t] (-110496 G'[t]+97436 H'[t])-11110 G''[t]+10190 H''[t])-501760 H[t] (G'[t] (19 G''[t]-41 H''[t])+H'[t] (-63 G''[t]+85 H''[t]))-11038720 G'[t] Derivative[3][G][t]+11038720 H'[t] Derivative[3][G][t]+3584 G[t] (6972 ((H[t])^5)+((H[t])^3) (6358 G'[t]-39258 H'[t])+170 ((H[t])^2) (207 G''[t]-187 H''[t])-140 (G'[t] (333 G''[t]-311 H''[t])+H'[t] (-289 G''[t]+267 H''[t]))+H[t] (-29077 ((G'[t])^2)+92834 G'[t] H'[t]-57597 ((H'[t])^2)-1240 (Derivative[3][G][t]-Derivative[3][H][t])))+3584 ((H[t])^2) (21033 ((G'[t])^2)-25526 G'[t] H'[t]+1413 ((H'[t])^2)+2160 (Derivative[3][G][t]-Derivative[3][H][t]))-3584 ((G[t])^2) (60597 ((H[t])^4)+98216 ((G'[t])^2)-145212 G'[t] H'[t]+50076 ((H'[t])^2)+((H[t])^2) (-149343 G'[t]+91003 H'[t])+10 H[t] (2249 G''[t]-2217 H''[t])+920 Derivative[3][G][t]-920 Derivative[3][H][t])+11038720 G'[t] Derivative[3][H][t]-11038720 H'[t] Derivative[3][H][t]))+(OverBar[Ψ])[t] (-7 G[t]-(1/10125)7 Γ (86016 ((G[t])^7)+132102656 ((G[t])^6) H[t]+17998848 G[t] ((H[t])^6)+29271552 G[t] ((G'[t])^3)-9216 G[t] ((H[t])^4) (601 G'[t]-3237 H'[t])-56749568 G[t] ((G'[t])^2) H'[t]-305664 G[t] ((H'[t])^3)-512 ((G[t])^5) (548181 ((H[t])^2)-265395 G'[t]+193841 H'[t])+3102720 G[t] ((G''[t])^2)+512 ((G[t])^4) (229311 ((H[t])^3)+H[t] (129429 G'[t]-211324 H'[t])+78423 G''[t]-73490 H''[t])+9216 G[t] ((H[t])^3) (1418 G''[t]-325 H''[t])-6205440 G[t] G''[t] H''[t]+3102720 G[t] ((H''[t])^2)-1024 G[t] H[t] (G'[t] (5361 G''[t]+2680 H''[t])-H'[t] (851 G''[t]+7190 H''[t]))-512 (17604 ((H[t])^5) G'[t]-144 ((H[t])^3) G'[t] (156 G'[t]-131 H'[t])+H[t] G'[t] (3851 ((G'[t])^2)-3602 G'[t] H'[t]-249 ((H'[t])^2))+5868 ((H[t])^4) G''[t]-41 (G'[t]-H'[t]) (-23 H'[t] G''[t]+G'[t] (123 G''[t]-100 H''[t]))-36 ((H[t])^2) (-113 H'[t] G''[t]+G'[t] (13 G''[t]+100 H''[t])))-3102720 G[t] H'[t] Derivative[3][G][t]-512 ((G[t])^2) (162648 ((H[t])^5)+((H[t])^3) (-304407 G'[t]+285278 H'[t])+2 H'[t] (53357 G''[t]-47350 H''[t])+((H[t])^2) (51981 G''[t]-35170 H''[t])+2 G'[t] (-59667 G''[t]+53660 H''[t])+H[t] (35691 ((G'[t])^2)+14712 G'[t] H'[t]-40883 ((H'[t])^2)+5520 (Derivative[3][G][t]-Derivative[3][H][t])))-512 G[t] ((H[t])^2) (80109 ((G'[t])^2)-68046 G'[t] H'[t]-11423 ((H'[t])^2)+270 (Derivative[3][G][t]-Derivative[3][H][t]))+2560 G[t] G'[t] (10853 ((H'[t])^2)+1212 (Derivative[3][G][t]-Derivative[3][H][t]))+512 ((G[t])^3) (188183 ((H[t])^4)+359976 ((G'[t])^2)-567750 G'[t] H'[t]+214334 ((H'[t])^2)+((H[t])^2) (-670809 G'[t]+632177 H'[t])+H[t] (-46098 G''[t]+44170 H''[t])+5790 Derivative[3][G][t]-5790 Derivative[3][H][t])+3102720 G[t] H'[t] Derivative[3][H][t]))+χ[t] (((23625 G[t]+3375 H[t])/3375)+(1/3375)Γ (200704 ((G[t])^7)+308435456 ((G[t])^6) H[t]+40857600 G[t] ((H[t])^6)+2021376 ((H[t])^7)+68300288 G[t] ((G'[t])^3)+5053440 H[t] ((G'[t])^3)-14336 G[t] ((H[t])^4) (20927 G'[t]-19996 H'[t])-68597760 G[t] ((G'[t])^2) H'[t]+14117376 H[t] ((G'[t])^2) H'[t]+45925376 G[t] ((H'[t])^3)+46301696 H[t] ((H'[t])^3)+21504 ((H[t])^5) (666 G'[t]+1595 H'[t])-3584 ((G[t])^5) (234744 ((H[t])^2)-88465 G'[t]+62334 H'[t])+7239680 G[t] ((G''[t])^2)+3799040 H[t] ((G''[t])^2)+3584 (G'[t]-H'[t]) (H'[t] (4479 G''[t]-6019 H''[t])+G'[t] (1681 G''[t]-141 H''[t]))+3584 ((G[t])^4) (260466 ((H[t])^3)-H[t] (13376 G'[t]+21911 H'[t])+26141 G''[t]-24171 H''[t])-7168 G[t] ((H[t])^3) (8231 G''[t]-5461 H''[t])-21504 ((H[t])^4) (921 G''[t]-1376 H''[t])-14479360 G[t] G''[t] H''[t]-7598080 H[t] G''[t] H''[t]+7239680 G[t] ((H''[t])^2)+3799040 H[t] ((H''[t])^2)+100352 ((H[t])^2) (G'[t] (317 G''[t]-432 H''[t])+H'[t] (-547 G''[t]+662 H''[t]))+7168 G[t] H[t] (G'[t] (3393 G''[t]-3253 H''[t])+H'[t] (-3113 G''[t]+2973 H''[t]))-7239680 G[t] H'[t] Derivative[3][G][t]+3584 ((G[t])^2) (24887 ((H[t])^5)+3 ((H[t])^3) (33434 G'[t]-38859 H'[t])+G'[t] (39778 G''[t]-36838 H''[t])+((H[t])^2) (26363 G''[t]-21503 H''[t])+2 H'[t] (-16949 G''[t]+15479 H''[t])+H[t] (-16903 ((G'[t])^2)+5724 G'[t] H'[t]+8839 ((H'[t])^2)-2850 (Derivative[3][G][t]-Derivative[3][H][t])))-3584 ((G[t])^3) (148688 ((H[t])^4)+((H[t])^2) (95679 G'[t]-111268 H'[t])+12 H[t] (2543 G''[t]-2208 H''[t])-2 (59996 ((G'[t])^2)-86748 G'[t] H'[t]+28682 ((H'[t])^2)+965 (Derivative[3][G][t]-Derivative[3][H][t])))-3584 G[t] G'[t] (12731 ((H'[t])^2)-2020 (Derivative[3][G][t]-Derivative[3][H][t]))-14336 H[t] G'[t] (4567 ((H'[t])^2)-265 (Derivative[3][G][t]-Derivative[3][H][t]))+35840 G[t] ((H[t])^2) (3498 ((G'[t])^2)-8082 G'[t] H'[t]+3894 ((H'[t])^2)+299 (Derivative[3][G][t]-Derivative[3][H][t]))-3584 ((H[t])^3) (2549 ((G'[t])^2)+22448 G'[t] H'[t]-30377 ((H'[t])^2)+2070 (Derivative[3][G][t]-Derivative[3][H][t]))-3799040 H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])+7239680 G[t] H'[t] Derivative[3][H][t]))+Ψ[t] (-H[t]+(1/10125)Γ (-587776 ((G[t])^6) H[t]+3419136 G[t] ((H[t])^6)-6064128 ((H[t])^7)-28962304 H[t] ((G'[t])^3)+3584 ((G[t])^4) H[t] (169557 G'[t]-145591 H'[t])-29442560 H[t] ((G'[t])^2) H'[t]-138905088 H[t] ((H'[t])^3)-10752 ((H[t])^5) (79103 ((G[t])^2)+9864 G'[t]+9570 H'[t])-11397120 H[t] ((G''[t])^2)+3584 ((H[t])^4) (634247 ((G[t])^3)+6 G[t] (40051 G'[t]-30281 H'[t])+18 (595 G''[t]-1376 H''[t]))+7168 ((G[t])^3) H[t] (22725 G''[t]-17659 H''[t])+22794240 H[t] G''[t] H''[t]-11397120 H[t] ((H''[t])^2)-7168 G[t] H[t] (G'[t] (15540 G''[t]-7079 H''[t])+H'[t] (-10190 G''[t]+1729 H''[t]))-3584 (6839 ((G[t])^5) H'[t]+2 ((G[t])^3) (23631 G'[t]-21121 H'[t]) H'[t]+G[t] H'[t] (53419 ((G'[t])^2)-92458 G'[t] H'[t]+39039 ((H'[t])^2))+977 ((G[t])^4) H''[t]+2 ((G[t])^2) (H'[t] (2510 G''[t]-913 H''[t])-1597 G'[t] H''[t])+(G'[t]-H'[t]) (H'[t] (14380 G''[t]-18057 H''[t])+3677 G'[t] H''[t]))+3584 ((H[t])^2) (156051 ((G[t])^5)+((G[t])^3) (-383772 G'[t]+298373 H'[t])+24 H'[t] (1745 G''[t]-2317 H''[t])-48 G'[t] (545 G''[t]-831 H''[t])+((G[t])^2) (-131070 G''[t]+99679 H''[t])+G[t] (-185049 ((G'[t])^2)+310506 G'[t] H'[t]-105397 ((H'[t])^2)-9240 (Derivative[3][G][t]-Derivative[3][H][t])))+10752 H[t] G'[t] (18351 ((H'[t])^2)-1060 (Derivative[3][G][t]-Derivative[3][H][t]))+7168 ((G[t])^2) H[t] (7509 ((G'[t])^2)-15942 G'[t] H'[t]+7183 ((H'[t])^2)+1515 (Derivative[3][G][t]-Derivative[3][H][t]))+11397120 H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])-3584 ((H[t])^3) (552087 ((G[t])^4)-30111 ((G'[t])^2)-48480 G'[t] H'[t]+91131 ((H'[t])^2)-((G[t])^2) (3501 G'[t]+64453 H'[t])+G[t] (-74910 G''[t]+38616 H''[t])-6210 Derivative[3][G][t]+6210 Derivative[3][H][t])))+α[t] (-1+(1/2025)Γ (-114688 ((G[t])^6)+74937856 ((G[t])^5) H[t]+15611904 ((H[t])^6)+28732928 ((G'[t])^3)-64512 ((H[t])^4) (188 G'[t]-377 H'[t])-49771008 ((G'[t])^2) H'[t]+13343232 G'[t] ((H'[t])^2)+7694848 ((H'[t])^3)-3584 ((G[t])^4) (3699 ((H[t])^2)-20297 G'[t]+13459 H'[t])+6623232 ((G''[t])^2)-193536 ((H[t])^3) (17 G''[t]-41 H''[t])-13246464 G''[t] H''[t]+6623232 ((H''[t])^2)-3584 ((G[t])^3) (66649 ((H[t])^3)+H[t] (-91616 G'[t]+81344 H'[t])-6766 G''[t]+6214 H''[t])+28672 H[t] (G'[t] (559 G''[t]-790 H''[t])+H'[t] (-1021 G''[t]+1252 H''[t]))+6623232 G'[t] Derivative[3][G][t]-6623232 H'[t] Derivative[3][G][t]+3584 ((G[t])^2) (65275 ((H[t])^4)+((H[t])^2) (-116299 G'[t]+78643 H'[t])+2 H[t] (7559 G''[t]-7463 H''[t])+8 (8245 ((G'[t])^2)-12408 G'[t] H'[t]+4394 ((H'[t])^2)+69 Derivative[3][G][t]-69 Derivative[3][H][t]))-3584 ((H[t])^2) (7999 ((G'[t])^2)-606 G'[t] H'[t]-9241 ((H'[t])^2)+1296 (Derivative[3][G][t]-Derivative[3][H][t]))-6623232 G'[t] Derivative[3][H][t]+6623232 H'[t] Derivative[3][H][t]-3584 G[t] (20160 ((H[t])^5)-2 ((H[t])^3) (3885 G'[t]+4687 H'[t])+2 ((H[t])^2) (10483 G''[t]-9463 H''[t])-8 (G'[t] (3599 G''[t]-3368 H''[t])+H'[t] (-3137 G''[t]+2906 H''[t]))+H[t] (-23351 ((G'[t])^2)+63966 G'[t] H'[t]-36919 ((H'[t])^2)-744 Derivative[3][G][t]+744 Derivative[3][H][t]))))-(14336/675) Γ (2 ((G[t])^4)+38 ((G[t])^3) H[t]+33 ((H[t])^4)+((G[t])^2) (-49 ((H[t])^2)+46 (G'[t]-H'[t]))+G[t] (-24 ((H[t])^3)+62 H[t] (G'[t]-H'[t]))-108 ((H[t])^2) (G'[t]-H'[t])+77 (((G'[t]-H'[t]))^2)) Derivative[3][χ][t];

(* E4Zero *)

E4Zero=(1/((a[t])^4))(k^4) (-(1/10125)512 Γ α[t] (-1897 ((G[t])^4)-11578 ((G[t])^3) H[t]+37919 ((G[t])^2) ((H[t])^2)-33516 G[t] ((H[t])^3)+9072 ((H[t])^4)-19166 ((G[t])^2) (G'[t]-H'[t])+21938 G[t] H[t] (G'[t]-H'[t])-2772 ((H[t])^2) (G'[t]-H'[t])-8197 (((G'[t]-H'[t]))^2))-(1/10125)512 Γ (OverBar[Ψ])[t] (-13279 ((G[t])^5)+64694 ((G[t])^4) H[t]-130627 ((G[t])^3) ((H[t])^2)+120288 ((G[t])^2) ((H[t])^3)-41076 G[t] ((H[t])^4)+11578 ((G[t])^3) (G'[t]-H'[t])-55594 ((G[t])^2) H[t] (G'[t]-H'[t])+44016 G[t] ((H[t])^2) (G'[t]-H'[t])-16219 G[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ χ[t] (13279 ((G[t])^5)-79870 ((G[t])^4) H[t]+183743 ((G[t])^3) ((H[t])^2)-212996 ((G[t])^2) ((H[t])^3)+127848 G[t] ((H[t])^4)-32004 ((H[t])^5)-11578 ((G[t])^3) (G'[t]-H'[t])+48006 ((G[t])^2) H[t] (G'[t]-H'[t])-77672 G[t] ((H[t])^2) (G'[t]-H'[t])+41244 ((H[t])^3) (G'[t]-H'[t])+16219 G[t] (((G'[t]-H'[t]))^2)-24416 H[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ Ψ[t] (15176 ((G[t])^4) H[t]-53116 ((G[t])^3) ((H[t])^2)+92708 ((G[t])^2) ((H[t])^3)-86772 G[t] ((H[t])^4)+32004 ((H[t])^5)+7588 ((G[t])^2) H[t] (G'[t]-H'[t])+33656 G[t] ((H[t])^2) (G'[t]-H'[t])-41244 ((H[t])^3) (G'[t]-H'[t])+24416 H[t] (((G'[t]-H'[t]))^2))-(1/10125)512 Γ (1897 ((G[t])^4)+11578 ((G[t])^3) H[t]-37919 ((G[t])^2) ((H[t])^2)+33516 G[t] ((H[t])^3)-9072 ((H[t])^4)+19166 ((G[t])^2) (G'[t]-H'[t])-21938 G[t] H[t] (G'[t]-H'[t])+2772 ((H[t])^2) (G'[t]-H'[t])+8197 (((G'[t]-H'[t]))^2)) χ'[t])-(1/3375)7168 Γ (14055 ((G[t])^6)-55038 ((G[t])^5) H[t]+((G[t])^4) (88056 ((H[t])^2)+20859 G'[t]-19577 H'[t])+((G[t])^3) (-68622 ((H[t])^3)-5 H[t] (8621 G'[t]-8141 H'[t])+1282 (G''[t]-H''[t]))+((G[t])^2) (17085 ((H[t])^4)+((H[t])^2) (38261 G'[t]-38753 H'[t])+2 (7679 ((G'[t])^2)-13994 G'[t] H'[t]+6315 ((H'[t])^2))-1118 H[t] (G''[t]-H''[t]))+G[t] (10332 ((H[t])^5)+((H[t])^3) (-30643 G'[t]+33699 H'[t])-2 H[t] (4105 ((G'[t])^2)-5482 G'[t] H'[t]+1377 ((H'[t])^2))-1610 ((H[t])^2) (G''[t]-H''[t])+2728 (G'[t]-H'[t]) (G''[t]-H''[t]))-2 (2934 ((H[t])^6)-1364 (((G'[t]-H'[t]))^3)+((H[t])^4) (-7314 G'[t]+8037 H'[t])+((H[t])^2) (3574 ((G'[t])^2)-8512 G'[t] H'[t]+4938 ((H'[t])^2))-723 ((H[t])^3) (G''[t]-H''[t])+1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t]))) α''[t]+(OverBar[Ψ])''[t] (-7 G[t]+(1/3375)7 Γ (53710336 ((G[t])^7)-98278400 ((G[t])^6) H[t]-2995200 G[t] ((H[t])^6)+47804416 G[t] ((G'[t])^3)-3072 G[t] ((H[t])^4) (5924 G'[t]-10503 H'[t])-85254144 G[t] ((G'[t])^2) H'[t]+1974272 G[t] ((H'[t])^3)-1024 ((G[t])^5) (34202 ((H[t])^2)-176446 G'[t]+110611 H'[t])+1396736 G[t] ((G''[t])^2)+1024 ((G[t])^4) (231204 ((H[t])^3)+H[t] (-325348 G'[t]+147162 H'[t])+22733 G''[t]-16470 H''[t])-58368 G[t] ((H[t])^3) (511 G''[t]-188 H''[t])-2793472 G[t] G''[t] H''[t]+1396736 G[t] ((H''[t])^2)+4096 G[t] H[t] (G'[t] (2033 G''[t]-2251 H''[t])+2 H'[t] (-1296 G''[t]+1405 H''[t]))+3072 (4890 ((H[t])^5) G'[t]+3 ((H[t])^3) G'[t] (-3331 G'[t]+3813 H'[t])+2 H[t] G'[t] (1787 ((G'[t])^2)-4938 G'[t] H'[t]+3151 ((H'[t])^2))+1956 ((H[t])^4) G''[t]+1364 (G'[t]-H'[t]) (-H'[t] G''[t]+G'[t] (3 G''[t]-2 H''[t]))+1446 ((H[t])^2) (H'[t] G''[t]+G'[t] (-2 G''[t]+H''[t])))-1396736 G[t] H'[t] Derivative[3][G][t]+1024 ((G[t])^2) (90531 ((H[t])^5)+((H[t])^3) (-158242 G'[t]+40242 H'[t])+((H[t])^2) (33375 G''[t]-7894 H''[t])+10 G'[t] (3328 G''[t]-2807 H''[t])+2 H'[t] (-13353 G''[t]+10748 H''[t])+H[t] (-34557 ((G'[t])^2)+6965 G'[t] H'[t]+21510 ((H'[t])^2)+82 Derivative[3][G][t]-82 Derivative[3][H][t]))+512 G[t] ((H[t])^2) (62805 ((G'[t])^2)-125666 G'[t] H'[t]+55929 ((H'[t])^2)-1446 (Derivative[3][G][t]-Derivative[3][H][t]))+4096 G[t] G'[t] (8661 ((H'[t])^2)+341 (Derivative[3][G][t]-Derivative[3][H][t]))+1396736 G[t] H'[t] Derivative[3][H][t]-512 ((G[t])^3) (482169 ((H[t])^4)-274959 ((G'[t])^2)+374282 G'[t] H'[t]-109743 ((H'[t])^2)+((H[t])^2) (-620492 G'[t]+216604 H'[t])+H[t] (65698 G''[t]-27296 H''[t])-1282 Derivative[3][G][t]+1282 Derivative[3][H][t])))+α[t] (((2 (94500 ((G[t])^2)+47250 G[t] H[t]+10125 ((H[t])^2)+23625 G'[t]+6750 H'[t]))/3375)+(1/3375)2 Γ (587776 ((G[t])^8)-1512706048 ((G[t])^7) H[t]-825108480 ((G[t])^2) ((H[t])^6)+588349440 G[t] ((H[t])^7)-35997696 ((H[t])^8)-823330816 ((G[t])^2) ((G'[t])^3)-77070336 G[t] H[t] ((G'[t])^3)-96868352 ((H[t])^2) ((G'[t])^3)-59508736 ((G'[t])^4)+43008 ((G[t])^2) ((H[t])^4) (160723 G'[t]-156060 H'[t])-774144 G[t] ((H[t])^5) (3353 G'[t]-2521 H'[t])+2002079744 ((G[t])^2) ((G'[t])^2) H'[t]+463081472 G[t] H[t] ((G'[t])^2) H'[t]+526647296 ((H[t])^2) ((G'[t])^2) H'[t]+140263424 ((G'[t])^3) H'[t]-63737856 ((G'[t])^2) ((H'[t])^2)+394526720 ((G[t])^2) ((H'[t])^3)+230723584 G[t] H[t] ((H'[t])^3)+372019200 ((H[t])^2) ((H'[t])^3)-55279616 G'[t] ((H'[t])^3)+38262784 ((H'[t])^4)+258048 ((H[t])^6) (325 G'[t]+606 H'[t])+14336 ((G[t])^6) (462237 ((H[t])^2)-104903 G'[t]+76752 H'[t])-18378752 ((G[t])^2) ((G''[t])^2)-2351104 G[t] H[t] ((G''[t])^2)+20729856 ((H[t])^2) ((G''[t])^2)-39108608 G'[t] ((G''[t])^2)+39108608 H'[t] ((G''[t])^2)-28672 ((G[t])^5) (402256 ((H[t])^3)-8725 H[t] (11 G'[t]-5 H'[t])+937 (15 G''[t]-14 H''[t]))+286720 ((G[t])^2) ((H[t])^3) (2593 G''[t]-1836 H''[t])+86016 G[t] ((H[t])^4) (425 G''[t]-1814 H''[t])-28041216 ((H[t])^5) (5 G''[t]-6 H''[t])+36757504 ((G[t])^2) G''[t] H''[t]+4702208 G[t] H[t] G''[t] H''[t]-41459712 ((H[t])^2) G''[t] H''[t]+78217216 G'[t] G''[t] H''[t]-78217216 H'[t] G''[t] H''[t]-18378752 ((G[t])^2) ((H''[t])^2)-2351104 G[t] H[t] ((H''[t])^2)+20729856 ((H[t])^2) ((H''[t])^2)-39108608 G'[t] ((H''[t])^2)+39108608 H'[t] ((H''[t])^2)-57344 H[t] (G'[t]-H'[t]) (G'[t] (1787 G''[t]-2128 H''[t])+H'[t] (-3151 G''[t]+3492 H''[t]))+86016 ((H[t])^3) (G'[t] (3331 G''[t]-3572 H''[t])+H'[t] (-3813 G''[t]+4054 H''[t]))-57344 G[t] (G'[t]-H'[t]) (G'[t] (6397 G''[t]-6056 H''[t])+H'[t] (-5033 G''[t]+4692 H''[t]))-28672 G[t] ((H[t])^2) (G'[t] (7089 G''[t]-7894 H''[t])+H'[t] (-8699 G''[t]+9504 H''[t]))+28672 ((G[t])^2) H[t] (G'[t] (14207 G''[t]-13648 H''[t])+H'[t] (-13089 G''[t]+12530 H''[t]))-19554304 ((G'[t])^2) Derivative[3][G][t]+18378752 ((G[t])^2) H'[t] Derivative[3][G][t]+39108608 G'[t] H'[t] Derivative[3][G][t]-19554304 ((H'[t])^2) Derivative[3][G][t]-28672 ((G[t])^3) (97197 ((H[t])^5)+((H[t])^3) (231204 G'[t]-275290 H'[t])+G'[t] (17111 G''[t]-16470 H''[t])+52 ((H[t])^2) (965 G''[t]-821 H''[t])+H'[t] (-15829 G''[t]+15188 H''[t])+H[t] (-99794 ((G'[t])^2)+147162 G'[t] H'[t]-48568 ((H'[t])^2)-3107 (Derivative[3][G][t]-Derivative[3][H][t])))+43008 ((H[t])^4) (4649 ((G'[t])^2)-21006 G'[t] H'[t]+16839 ((H'[t])^2)-652 (Derivative[3][G][t]-Derivative[3][H][t]))-43008 ((H[t])^2) G'[t] (18643 ((H'[t])^2)-482 (Derivative[3][G][t]-Derivative[3][H][t]))-57344 G[t] H[t] G'[t] (10755 ((H'[t])^2)+41 (Derivative[3][G][t]-Derivative[3][H][t]))-14336 ((G[t])^2) G'[t] (109743 ((H'[t])^2)+1282 (Derivative[3][G][t]-Derivative[3][H][t]))+28672 G[t] ((H[t])^3) (40226 ((G'[t])^2)-40242 G'[t] H'[t]-1512 ((H'[t])^2)+3189 (Derivative[3][G][t]-Derivative[3][H][t]))-28672 ((G[t])^2) ((H[t])^2) (79853 ((G'[t])^2)-108302 G'[t] H'[t]+28203 ((H'[t])^2)+4381 (Derivative[3][G][t]-Derivative[3][H][t]))+2351104 G[t] H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])-20729856 ((H[t])^2) H'[t] (Derivative[3][G][t]-Derivative[3][H][t])+19554304 ((G'[t])^2) Derivative[3][H][t]-18378752 ((G[t])^2) H'[t] Derivative[3][H][t]-39108608 G'[t] H'[t] Derivative[3][H][t]+19554304 ((H'[t])^2) Derivative[3][H][t]+14336 ((G[t])^4) (661172 ((H[t])^4)-134281 ((G'[t])^2)+4 ((H[t])^2) (17101 G'[t]-54736 H'[t])+221222 G'[t] H'[t]-88223 ((H'[t])^2)+8 H[t] (10480 G''[t]-9469 H''[t])-1874 Derivative[3][G][t]+1874 Derivative[3][H][t])))+α'[t] (((23625 G[t]+6750 H[t])/3375)+(1/3375)Γ (-375972352 ((G[t])^7)+963027968 ((G[t])^6) H[t]+508870656 G[t] ((H[t])^6)+39094272 ((H[t])^7)-334630912 G[t] ((G'[t])^3)-41789440 H[t] ((G'[t])^3)-7168 ((G[t])^5) (9423 ((H[t])^2)+176446 G'[t]-149965 H'[t])-64512 ((H[t])^5) (5131 G'[t]-7569 H'[t])+857235456 G[t] ((G'[t])^2) H'[t]+272025600 H[t] ((G'[t])^2) H'[t]+187973632 G[t] ((H'[t])^3)+188446720 H[t] ((H'[t])^3)-21504 G[t] ((H[t])^4) (7490 G'[t]+16953 H'[t])-9777152 G[t] ((G''[t])^2)+9777152 H[t] ((G''[t])^2)-7168 ((G[t])^4) (340676 ((H[t])^3)+H[t] (-435959 G'[t]+349013 H'[t])+22733 G''[t]-22092 H''[t])+14336 G[t] ((H[t])^3) (18913 G''[t]-19677 H''[t])-21504 ((H[t])^4) (5769 G''[t]-6010 H''[t])-87994368 (((G'[t]-H'[t]))^2) (G''[t]-H''[t])+19554304 G[t] G''[t] H''[t]-19554304 H[t] G''[t] H''[t]-9777152 G[t] ((H''[t])^2)+9777152 H[t] ((H''[t])^2)+57344 G[t] H[t] (G'[t] (1841 G''[t]-1500 H''[t])+H'[t] (-1159 G''[t]+818 H''[t]))+28672 ((H[t])^2) (G'[t] (4638 G''[t]-4979 H''[t])+H'[t] (-5320 G''[t]+5661 H''[t]))+9777152 G[t] H'[t] Derivative[3][G][t]-7168 ((G[t])^2) (324621 ((H[t])^5)-48 ((H[t])^3) (5553 G'[t]-3161 H'[t])+4 G'[t] (8320 G''[t]-7979 H''[t])+6 ((H[t])^2) (7744 G''[t]-7785 H''[t])+4 H'[t] (-7638 G''[t]+7297 H''[t])+H[t] (-104384 ((G'[t])^2)+157652 G'[t] H'[t]-57360 ((H'[t])^2)-559 (Derivative[3][G][t]-Derivative[3][H][t])))-3584 G[t] ((H[t])^2) (30503 ((G'[t])^2)-86990 G'[t] H'[t]+64671 ((H'[t])^2)-1610 (Derivative[3][G][t]-Derivative[3][H][t]))+7168 ((H[t])^3) (48347 ((G'[t])^2)-122394 G'[t] H'[t]+75411 ((H'[t])^2)-723 (Derivative[3][G][t]-Derivative[3][H][t]))-315392 G[t] G'[t] (2253 ((H'[t])^2)+31 (Derivative[3][G][t]-Derivative[3][H][t]))-9777152 H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])-9777152 G[t] H'[t] Derivative[3][H][t]+3584 ((G[t])^3) (1032749 ((H[t])^4)-274959 ((G'[t])^2)+473102 G'[t] H'[t]-200871 ((H'[t])^2)+((H[t])^2) (-914816 G'[t]+667028 H'[t])+12 H[t] (8113 G''[t]-7913 H''[t])-1282 Derivative[3][G][t]+1282 Derivative[3][H][t])-157696 H[t] G'[t] (2655 ((H'[t])^2)+62 (-Derivative[3][G][t]+Derivative[3][H][t]))))+Ψ''[t] (-2 H[t]-(1/3375)2 Γ (137539584 ((G[t])^6) H[t]+243952128 G[t] ((H[t])^6)+19547136 ((H[t])^7)+17532928 H[t] ((G'[t])^3)+3584 ((G[t])^4) H[t] (110611 G'[t]-201851 H'[t])-290304 ((H[t])^5) (2890 ((G[t])^2)+389 G'[t]-841 H'[t])+29826048 H[t] ((G'[t])^2) H'[t]+94223360 H[t] ((H'[t])^3)+4888576 H[t] ((G''[t])^2)+3584 ((G[t])^3) H[t] (15829 G''[t]-33830 H''[t])-9777152 H[t] G''[t] H''[t]+4888576 H[t] ((H''[t])^2)+3584 ((H[t])^4) (275290 ((G[t])^3)-6 G[t] (6707 G'[t]+3225 H'[t])-11439 G''[t]+18030 H''[t])+14336 G[t] H[t] (G'[t] (5715 G''[t]-5251 H''[t])+2 H'[t] (-2455 G''[t]+2223 H''[t]))+21504 (6559 ((G[t])^5) H'[t]+((G[t])^3) (8235 G'[t]-7594 H'[t]) H'[t]+4 G[t] H'[t] (1514 ((G'[t])^2)-2687 G'[t] H'[t]+1173 ((H'[t])^2))+937 ((G[t])^4) H''[t]+682 (G'[t]-H'[t]) (H'[t] (2 G''[t]-3 H''[t])+G'[t] H''[t])+641 ((G[t])^2) (H'[t] (G''[t]-2 H''[t])+G'[t] H''[t]))-4888576 H[t] H'[t] Derivative[3][G][t]-14336 H[t] G'[t] (9876 ((H'[t])^2)-341 (Derivative[3][G][t]-Derivative[3][H][t]))+3584 ((G[t])^2) H[t] (69827 ((G'[t])^2)-150687 G'[t] H'[t]+78870 ((H'[t])^2)+641 (Derivative[3][G][t]-Derivative[3][H][t]))-3584 ((H[t])^3) (109472 ((G[t])^4)-18368 ((G'[t])^2)-2 ((G[t])^2) (54151 G'[t]-55743 H'[t])+88077 G'[t] H'[t]-75411 ((H'[t])^2)+G[t] (-8699 G''[t]+28638 H''[t])+723 Derivative[3][G][t]-723 Derivative[3][H][t])+4888576 H[t] H'[t] Derivative[3][H][t]-3584 ((H[t])^2) (43625 ((G[t])^5)+2 ((G[t])^3) (73581 G'[t]-112606 H'[t])+((G[t])^2) (13089 G''[t]-38816 H''[t])+2 H'[t] (8471 G''[t]-11322 H''[t])+G'[t] (-9876 G''[t]+15578 H''[t])+G[t] (-16151 ((G'[t])^2)+19338 G'[t] H'[t]+4371 ((H'[t])^2)-82 Derivative[3][G][t]+82 Derivative[3][H][t]))))+(OverBar[Ψ])'[t] (-((14 (13500 ((G[t])^2)+3375 G[t] H[t]+3375 G'[t]))/3375)-(1/3375)14 Γ (83968 ((G[t])^8)-189088256 ((G[t])^7) H[t]-29468160 ((G[t])^2) ((H[t])^6)+10506240 G[t] ((H[t])^7)+2995200 ((H[t])^6) G'[t]-117618688 ((G[t])^2) ((G'[t])^3)-9633792 G[t] H[t] ((G'[t])^3)-8501248 ((G'[t])^4)+3072 ((G[t])^2) ((H[t])^4) (160723 G'[t]-78030 H'[t])-1536 ((G'[t])^3) (6757 ((H[t])^2)-9784 H'[t])-13824 G[t] ((H[t])^5) (10059 G'[t]-2521 H'[t])-32265216 ((H[t])^4) G'[t] H'[t]+214508544 ((G[t])^2) ((G'[t])^2) H'[t]+41346560 G[t] H[t] ((G'[t])^2) H'[t]+14090240 ((G[t])^2) ((H'[t])^3)+4120064 G[t] H[t] ((H'[t])^3)-1974272 G'[t] ((H'[t])^3)+512 ((G[t])^6) (1386711 ((H[t])^2)-419612 G'[t]+230256 H'[t])-2625536 ((G[t])^2) ((G''[t])^2)-293888 G[t] H[t] ((G''[t])^2)-5586944 G'[t] ((G''[t])^2)-2560 ((G[t])^5) (402256 ((H[t])^3)-1745 H[t] (77 G'[t]-25 H'[t])+1874 (12 G''[t]-7 H''[t]))+1536 ((H[t])^3) G'[t] (16655 G''[t]-7144 H''[t])+5120 ((G[t])^2) ((H[t])^3) (12965 G''[t]-3672 H''[t])+10240 H[t] G'[t] H'[t] (2469 G''[t]-1124 H''[t])+3072 G[t] ((H[t])^4) (850 G''[t]-907 H''[t])+3281920 ((G[t])^2) G''[t] H''[t]+335872 G[t] H[t] G''[t] H''[t]+6983680 G'[t] G''[t] H''[t]-656384 ((G[t])^2) ((H''[t])^2)-41984 G[t] H[t] ((H''[t])^2)-1396736 G'[t] ((H''[t])^2)-1024 G[t] ((H[t])^2) (3 G'[t] (7089 G''[t]-3947 H''[t])+2 H'[t] (-8699 G''[t]+2376 H''[t]))-4096 G[t] (2 ((G'[t])^2) (6397 G''[t]-3785 H''[t])+((H'[t])^2) (5033 G''[t]-1173 H''[t])+3 G'[t] H'[t] (-5715 G''[t]+2687 H''[t]))+512 ((G[t])^2) H[t] (G'[t] (99449 G''[t]-54592 H''[t])+5 H'[t] (-13089 G''[t]+5012 H''[t]))+1969152 ((G[t])^2) H'[t] Derivative[3][G][t]-512 (14670 ((H[t])^5) G''[t]+34317 ((H[t])^3) H'[t] G''[t]+18906 H[t] ((H'[t])^2) G''[t]+3912 ((H[t])^4) Derivative[3][G][t]-1446 ((H[t])^2) (3 ((G''[t])^2)-3 G''[t] H''[t]-2 H'[t] Derivative[3][G][t])+2728 H'[t] (-3 ((G''[t])^2)+3 G''[t] H''[t]+H'[t] Derivative[3][G][t]))-1024 G[t] H[t] G'[t] (32265 ((H'[t])^2)+41 (7 Derivative[3][G][t]-3 Derivative[3][H][t]))-1024 ((G[t])^2) G'[t] (109743 ((H'[t])^2)+1282 (2 Derivative[3][G][t]-Derivative[3][H][t]))-1024 ((G[t])^2) ((H[t])^2) (239559 ((G'[t])^2)-216604 G'[t] H'[t]+28203 ((H'[t])^2)+4381 (3 Derivative[3][G][t]-Derivative[3][H][t]))+1396736 G'[t] H'[t] (3 Derivative[3][G][t]-Derivative[3][H][t])+41984 G[t] H[t] H'[t] (5 Derivative[3][G][t]-Derivative[3][H][t])-656384 ((G[t])^2) H'[t] Derivative[3][H][t]+1024 ((G[t])^4) (661172 ((H[t])^4)-268562 ((G'[t])^2)+2 ((H[t])^2) (51303 G'[t]-109472 H'[t])+331833 G'[t] H'[t]-88223 ((H'[t])^2)+8 H[t] (18340 G''[t]-9469 H''[t])-3748 Derivative[3][G][t]+1874 Derivative[3][H][t])+512 G[t] ((H[t])^3) (201130 ((G'[t])^2)-120726 G'[t] H'[t]-1512 ((H'[t])^2)-3189 (-5 Derivative[3][G][t]+Derivative[3][H][t]))-1536 ((H[t])^2) G'[t] (18643 ((H'[t])^2)+482 (-3 Derivative[3][G][t]+Derivative[3][H][t]))+1024 ((G'[t])^2) (13947 ((H[t])^4)+36736 ((H[t])^2) H'[t]-4446 ((H'[t])^2)+H[t] (-12509 G''[t]+8512 H''[t])+1364 (-2 Derivative[3][G][t]+Derivative[3][H][t]))-512 ((G[t])^3) (291591 ((H[t])^5)+30 ((H[t])^3) (38534 G'[t]-27529 H'[t])+2 G'[t] (68444 G''[t]-41175 H''[t])+156 ((H[t])^2) (1930 G''[t]-821 H''[t])+6 H'[t] (-15829 G''[t]+7594 H''[t])+H[t] (-698558 ((G'[t])^2)+735810 G'[t] H'[t]-145704 ((H'[t])^2)-21749 Derivative[3][G][t]+9321 Derivative[3][H][t]))))+Ψ'[t] (((2 (-23625 G[t] H[t]-10125 ((H[t])^2)-6750 H'[t]))/3375)+(1/3375)2 Γ (189088256 ((G[t])^7) H[t]-514805760 G[t] ((H[t])^7)+35997696 ((H[t])^8)+9633792 G[t] H[t] ((G'[t])^3)+24217088 ((H[t])^2) ((G'[t])^3)+677376 G[t] ((H[t])^5) (2395 G'[t]-2521 H'[t])-173655552 G[t] H[t] ((G'[t])^2) H'[t]-263323648 ((H[t])^2) ((G'[t])^2) H'[t]-35065856 ((G'[t])^3) H'[t]-201883136 G[t] H[t] ((H'[t])^3)-372019200 ((H[t])^2) ((H'[t])^3)+41459712 G'[t] ((H'[t])^3)-38262784 ((H'[t])^4)-193536 ((H[t])^6) (325 G'[t]+808 H'[t])-10752 ((G[t])^6) (154079 ((H[t])^2)+25584 H'[t])+293888 G[t] H[t] ((G''[t])^2)-5182464 ((H[t])^2) ((G''[t])^2)-9777152 H'[t] ((G''[t])^2)+7168 H[t] (((H'[t])^2) (15755 G''[t]-27936 H''[t])+((G'[t])^2) (1787 G''[t]-8512 H''[t])-6 G'[t] H'[t] (2469 G''[t]-5620 H''[t]))+3584 ((G[t])^5) (1206768 ((H[t])^3)-8725 H[t] (11 G'[t]-15 H'[t])-39354 H''[t])-21504 G[t] ((H[t])^4) (850 G''[t]-6349 H''[t])+3505152 ((H[t])^5) (25 G''[t]-48 H''[t])-2351104 G[t] H[t] G''[t] H''[t]+25912320 ((H[t])^2) G''[t] H''[t]+48885760 H'[t] G''[t] H''[t]+2057216 G[t] H[t] ((H''[t])^2)-20729856 ((H[t])^2) ((H''[t])^2)-39108608 H'[t] ((H''[t])^2)-28672 G[t] (5 G'[t] H'[t] (1143 G''[t]-2687 H''[t])+4542 ((G'[t])^2) H''[t]+7 ((H'[t])^2) (-719 G''[t]+1173 H''[t]))+7168 G[t] ((H[t])^2) (G'[t] (7089 G''[t]-19735 H''[t])+2 H'[t] (-8699 G''[t]+16632 H''[t]))-10752 ((H[t])^3) (3 G'[t] (3331 G''[t]-7144 H''[t])+H'[t] (-19065 G''[t]+32432 H''[t]))+3584 ((G[t])^3) (485985 ((H[t])^5)+2 ((H[t])^3) (346806 G'[t]-688225 H'[t])+260 ((H[t])^2) (386 G''[t]-821 H''[t])-49410 G'[t] H''[t]+H'[t] (-31658 G''[t]+75940 H''[t])+H[t] (-99794 ((G'[t])^2)+441486 G'[t] H'[t]-242840 ((H'[t])^2)-3107 (Derivative[3][G][t]-5 Derivative[3][H][t])))-10752 G[t] ((H[t])^3) (40226 ((G'[t])^2)-67070 G'[t] H'[t]-3528 ((H'[t])^2)+1063 (3 Derivative[3][G][t]-7 Derivative[3][H][t]))+7168 G[t] H[t] G'[t] (53775 ((H'[t])^2)+41 (Derivative[3][G][t]-5 Derivative[3][H][t]))+10752 ((H[t])^2) G'[t] (55929 ((H'[t])^2)-482 (Derivative[3][G][t]-3 Derivative[3][H][t]))-21504 ((H[t])^4) (4649 ((G'[t])^2)-31509 G'[t] H'[t]+33678 ((H'[t])^2)-652 (Derivative[3][G][t]-2 Derivative[3][H][t]))+14336 ((H'[t])^2) (2223 ((G'[t])^2)+682 (Derivative[3][G][t]-2 Derivative[3][H][t]))-293888 G[t] H[t] H'[t] (3 Derivative[3][G][t]-7 Derivative[3][H][t])-9777152 G'[t] H'[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+10364928 ((H[t])^2) H'[t] (Derivative[3][G][t]-2 Derivative[3][H][t])-7168 ((G[t])^4) (661172 ((H[t])^4)+((H[t])^2) (34202 G'[t]-218944 H'[t])+110611 G'[t] H'[t]-88223 ((H'[t])^2)+8 H[t] (2620 G''[t]-9469 H''[t])+1874 Derivative[3][H][t])-9777152 G'[t] (3 G''[t] H''[t]-3 ((H''[t])^2)+G'[t] Derivative[3][H][t])+3584 ((G[t])^2) (172665 ((H[t])^6)+((H[t])^4) (-964338 G'[t]+1404540 H'[t])-30 ((H[t])^3) (2593 G''[t]-3672 H''[t])+H[t] (3 H'[t] (13089 G''[t]-25060 H''[t])+G'[t] (-14207 G''[t]+54592 H''[t]))+2 ((H[t])^2) (79853 ((G'[t])^2)-216604 G'[t] H'[t]+84609 ((H'[t])^2)+4381 (Derivative[3][G][t]-3 Derivative[3][H][t]))-2 (69827 ((G'[t])^2) H'[t]+41280 ((H'[t])^3)+1923 (G''[t]-H''[t]) H''[t]+641 H'[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+G'[t] (-109743 ((H'[t])^2)+1282 Derivative[3][H][t])))))-(1/3375)7168 Γ (G[t]-H[t]) (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[3][α][t]+(1/((a[t])^2))(k^2) ((1/10125)Γ α'[t] (-100154880 ((G[t])^5)+413790720 ((G[t])^4) H[t]-668398080 ((G[t])^3) ((H[t])^2)+533460480 ((G[t])^2) ((H[t])^3)-216115200 G[t] ((H[t])^4)+37416960 ((H[t])^5)-40972288 ((G[t])^3) G'[t]+105025536 ((G[t])^2) H[t] G'[t]-65687552 G[t] ((H[t])^2) G'[t]+1634304 ((H[t])^3) G'[t]-512512 G[t] ((G'[t])^2)+12497408 H[t] ((G'[t])^2)+38377472 ((G[t])^3) H'[t]-94717952 ((G[t])^2) H[t] H'[t]+52856832 G[t] ((H[t])^2) H'[t]+3483648 ((H[t])^3) H'[t]+3548160 G[t] G'[t] H'[t]-27517952 H[t] G'[t] H'[t]-3035648 G[t] ((H'[t])^2)+15020544 H[t] ((H'[t])^2)-5117952 ((H[t])^2) G''[t]+2523136 G'[t] G''[t]-2523136 H'[t] G''[t]-2594816 ((G[t])^2) (G''[t]-H''[t])+7712768 G[t] H[t] (G''[t]-H''[t])+5117952 ((H[t])^2) H''[t]-2523136 G'[t] H''[t]+2523136 H'[t] H''[t])+(1/10125)Γ (OverBar[Ψ])'[t] (111068160 ((G[t])^6)-591980032 ((G[t])^5) H[t]+1146693632 ((G[t])^4) ((H[t])^2)-940688896 ((G[t])^3) ((H[t])^3)+253876224 ((G[t])^2) ((H[t])^4)+21030912 G[t] ((H[t])^5)-75536384 ((G[t])^4) G'[t]+34141184 ((G[t])^3) H[t] G'[t]+374277120 ((G[t])^2) ((H[t])^2) G'[t]-417005568 G[t] ((H[t])^3) G'[t]+84123648 ((H[t])^4) G'[t]-46993408 ((G[t])^2) ((G'[t])^2)+196793856 G[t] H[t] ((G'[t])^2)-76167168 ((H[t])^2) ((G'[t])^2)+8307712 ((G'[t])^3)+73135104 ((G[t])^4) H'[t]-87313408 ((G[t])^3) H[t] H'[t]-176605184 ((G[t])^2) ((H[t])^2) H'[t]+190783488 G[t] ((H[t])^3) H'[t]+49874944 ((G[t])^2) G'[t] H'[t]-273308672 G[t] H[t] G'[t] H'[t]+76167168 ((H[t])^2) G'[t] H'[t]-16615424 ((G'[t])^2) H'[t]-2881536 ((G[t])^2) ((H'[t])^2)+76514816 G[t] H[t] ((H'[t])^2)+8307712 G'[t] ((H'[t])^2)-18665472 ((G[t])^3) G''[t]+52770816 ((G[t])^2) H[t] G''[t]-34105344 G[t] ((H[t])^2) G''[t]+15439872 G[t] G'[t] G''[t]-15439872 G[t] H'[t] G''[t]+18665472 ((G[t])^3) H''[t]-52770816 ((G[t])^2) H[t] H''[t]+34105344 G[t] ((H[t])^2) H''[t]-15439872 G[t] G'[t] H''[t]+15439872 G[t] H'[t] H''[t])+(1/10125)Γ Ψ'[t] (-10913280 ((G[t])^5) H[t]+178189312 ((G[t])^4) ((H[t])^2)-478295552 ((G[t])^3) ((H[t])^3)+407228416 ((G[t])^2) ((H[t])^4)-37761024 G[t] ((H[t])^5)-58447872 ((H[t])^6)+132772864 ((G[t])^3) H[t] G'[t]-263775232 ((G[t])^2) ((H[t])^2) G'[t]-24041472 G[t] ((H[t])^3) G'[t]+155043840 ((H[t])^4) G'[t]-12045824 G[t] H[t] ((G'[t])^2)-73572352 ((H[t])^2) ((G'[t])^2)-3118080 ((G[t])^4) H'[t]-36893696 ((G[t])^3) H[t] H'[t]-32686080 ((G[t])^2) ((H[t])^2) H'[t]+341798912 G[t] ((H[t])^3) H'[t]-269101056 ((H[t])^4) H'[t]+62146560 ((G[t])^2) G'[t] H'[t]-137303040 G[t] H[t] G'[t] H'[t]+246392832 ((H[t])^2) G'[t] H'[t]-9569280 ((G'[t])^2) H'[t]-62146560 ((G[t])^2) ((H'[t])^2)+149348864 G[t] H[t] ((H'[t])^2)-172820480 ((H[t])^2) ((H'[t])^2)+19138560 G'[t] ((H'[t])^2)-9569280 ((H'[t])^3)+21260288 ((G[t])^2) H[t] G''[t]-60483584 G[t] ((H[t])^2) G''[t]+39223296 ((H[t])^3) G''[t]-17963008 H[t] G'[t] G''[t]+17963008 H[t] H'[t] G''[t]-21260288 ((G[t])^2) H[t] H''[t]+60483584 G[t] ((H[t])^2) H''[t]-39223296 ((H[t])^3) H''[t]+17963008 H[t] G'[t] H''[t]-17963008 H[t] H'[t] H''[t])+(1/10125)Γ (-6573056 ((G[t])^4)+24994816 ((G[t])^3) H[t]-34915328 ((G[t])^2) ((H[t])^2)+21138432 G[t] ((H[t])^3)-4644864 ((H[t])^4)-1297408 ((G[t])^2) G'[t]+3856384 G[t] H[t] G'[t]-2558976 ((H[t])^2) G'[t]+630784 ((G'[t])^2)+1297408 ((G[t])^2) H'[t]-3856384 G[t] H[t] H'[t]+2558976 ((H[t])^2) H'[t]-1261568 G'[t] H'[t]+630784 ((H'[t])^2)) α''[t]+(1/10125)Γ (92022784 ((G[t])^5)-349927424 ((G[t])^4) H[t]+488814592 ((G[t])^3) ((H[t])^2)-295938048 ((G[t])^2) ((H[t])^3)+65028096 G[t] ((H[t])^4)+70748160 ((G[t])^3) G'[t]-203958272 ((G[t])^2) H[t] G'[t]+175486976 G[t] ((H[t])^2) G'[t]-42276864 ((H[t])^3) G'[t]-3641344 G[t] ((G'[t])^2)-7712768 H[t] ((G'[t])^2)-68153344 ((G[t])^3) H'[t]+193650688 ((G[t])^2) H[t] H'[t]-162656256 G[t] ((H[t])^2) H'[t]+37158912 ((H[t])^3) H'[t]+4759552 G[t] G'[t] H'[t]+17948672 H[t] G'[t] H'[t]-1118208 G[t] ((H'[t])^2)-10235904 H[t] ((H'[t])^2)+2594816 ((G[t])^2) G''[t]-7712768 G[t] H[t] G''[t]+5117952 ((H[t])^2) G''[t]-2523136 G'[t] G''[t]+2523136 H'[t] G''[t]-2594816 ((G[t])^2) H''[t]+7712768 G[t] H[t] H''[t]-5117952 ((H[t])^2) H''[t]+2523136 G'[t] H''[t]-2523136 H'[t] H''[t]) χ''[t]+(1/10125)Γ (-1559040 ((G[t])^4) H[t]+37309440 ((G[t])^3) ((H[t])^2)-107358720 ((G[t])^2) ((H[t])^3)+109025280 G[t] ((H[t])^4)-37416960 ((H[t])^5)+31073280 ((G[t])^2) H[t] G'[t]-71715840 G[t] ((H[t])^2) G'[t]+40642560 ((H[t])^3) G'[t]-4784640 H[t] ((G'[t])^2)-31073280 ((G[t])^2) H[t] H'[t]+71715840 G[t] ((H[t])^2) H'[t]-40642560 ((H[t])^3) H'[t]+9569280 H[t] G'[t] H'[t]-4784640 H[t] ((H'[t])^2)) Ψ''[t]+(1/10125)Γ (8132096 ((G[t])^5)-62304256 ((G[t])^4) H[t]+142274048 ((G[t])^3) ((H[t])^2)-130163712 ((G[t])^2) ((H[t])^3)+42061824 G[t] ((H[t])^4)-29775872 ((G[t])^3) G'[t]+67859456 ((G[t])^2) H[t] G'[t]-38083584 G[t] ((H[t])^2) G'[t]+4153856 G[t] ((G'[t])^2)+29775872 ((G[t])^3) H'[t]-67859456 ((G[t])^2) H[t] H'[t]+38083584 G[t] ((H[t])^2) H'[t]-8307712 G[t] G'[t] H'[t]+4153856 G[t] ((H'[t])^2)) (OverBar[Ψ])''[t]+χ'[t] (1+(1/10125)Γ (268083200 ((G[t])^6)-778233344 ((G[t])^5) H[t]+427646464 ((G[t])^4) ((H[t])^2)+720409088 ((G[t])^3) ((H[t])^3)-991882752 ((G[t])^2) ((H[t])^4)+394619904 G[t] ((H[t])^5)-40642560 ((H[t])^6)+667530752 ((G[t])^4) G'[t]-1923102720 ((G[t])^3) H[t] G'[t]+1758005760 ((G[t])^2) ((H[t])^2) G'[t]-484951040 G[t] ((H[t])^3) G'[t]-17482752 ((H[t])^4) G'[t]+148513792 ((G[t])^2) ((G'[t])^2)-335716864 G[t] H[t] ((G'[t])^2)+143678976 ((H[t])^2) ((G'[t])^2)-10569216 ((G'[t])^3)-587313664 ((G[t])^4) H'[t]+1614577664 ((G[t])^3) H[t] H'[t]-1333287424 ((G[t])^2) ((H[t])^2) H'[t]+240221184 G[t] ((H[t])^3) H'[t]+65802240 ((H[t])^4) H'[t]-293766144 ((G[t])^2) G'[t] H'[t]+637156352 G[t] H[t] G'[t] H'[t]-256342016 ((H[t])^2) G'[t] H'[t]+26030592 ((G'[t])^2) H'[t]+143990784 ((G[t])^2) ((H'[t])^2)-298916352 G[t] H[t] ((H'[t])^2)+111401472 ((H[t])^2) ((H'[t])^2)-20353536 G'[t] ((H'[t])^2)+4892160 ((H'[t])^3)+73644032 ((G[t])^3) G''[t]-211183616 ((G[t])^2) H[t] G''[t]+183773184 G[t] ((H[t])^2) G''[t]-46233600 ((H[t])^3) G''[t]-3225600 G[t] G'[t] G''[t]-16959488 H[t] G'[t] G''[t]+702464 G[t] H'[t] G''[t]+19482624 H[t] H'[t] G''[t]-1261568 ((G''[t])^2)-72346624 ((G[t])^3) H''[t]+206029824 ((G[t])^2) H[t] H''[t]-177357824 G[t] ((H[t])^2) H''[t]+43674624 ((H[t])^3) H''[t]+1964032 G[t] G'[t] H''[t]+18221056 H[t] G'[t] H''[t]+559104 G[t] H'[t] H''[t]-20744192 H[t] H'[t] H''[t]+2523136 G''[t] H''[t]-1261568 ((H''[t])^2)+1297408 ((G[t])^2) Derivative[3][G][t]-3856384 G[t] H[t] Derivative[3][G][t]+2558976 ((H[t])^2) Derivative[3][G][t]-1261568 G'[t] Derivative[3][G][t]+1261568 H'[t] Derivative[3][G][t]-1297408 ((G[t])^2) Derivative[3][H][t]+3856384 G[t] H[t] Derivative[3][H][t]-2558976 ((H[t])^2) Derivative[3][H][t]+1261568 G'[t] Derivative[3][H][t]-1261568 H'[t] Derivative[3][H][t]))+(OverBar[Ψ])[t] (-7 G[t]+(1/10125)Γ (377975808 ((G[t])^7)-3071004160 ((G[t])^6) H[t]+6790773248 ((G[t])^5) ((H[t])^2)-5723221504 ((G[t])^4) ((H[t])^3)+1279176192 ((G[t])^3) ((H[t])^4)+535385088 ((G[t])^2) ((H[t])^5)-189084672 G[t] ((H[t])^6)-1005007360 ((G[t])^5) G'[t]-563408384 ((G[t])^4) H[t] G'[t]+4633147904 ((G[t])^3) ((H[t])^2) G'[t]-4007295488 ((G[t])^2) ((H[t])^3) G'[t]+21030912 ((H[t])^5) G'[t]+1111746048 ((G[t])^2) H[t] ((G'[t])^2)-156678144 ((H[t])^3) ((G'[t])^2)-49032704 G[t] ((G'[t])^3)+61074944 H[t] ((G'[t])^3)+43008 G[t] ((H[t])^4) (21427 G'[t]-11829 H'[t])+735081984 ((G[t])^5) H'[t]+832434176 ((G[t])^4) H[t] H'[t]-3906570752 ((G[t])^3) ((H[t])^2) H'[t]+2847796224 ((G[t])^2) ((H[t])^3) H'[t]-1365704704 ((G[t])^2) H[t] G'[t] H'[t]+190783488 ((H[t])^3) G'[t] H'[t]+138510848 G[t] ((G'[t])^2) H'[t]-137589760 H[t] ((G'[t])^2) H'[t]+338698752 ((G[t])^2) H[t] ((H'[t])^2)-114483712 G[t] G'[t] ((H'[t])^2)+76514816 H[t] G'[t] ((H'[t])^2)+25005568 G[t] ((H'[t])^3)-394171904 ((G[t])^4) G''[t]+598391808 ((G[t])^3) H[t] G''[t]-78636544 ((G[t])^2) ((H[t])^2) G''[t]-167645184 G[t] ((H[t])^3) G''[t]+42061824 ((H[t])^4) G''[t]-244400128 ((G[t])^2) G'[t] G''[t]+196854784 G[t] H[t] G'[t] G''[t]-72188928 ((H[t])^2) G'[t] G''[t]+19593728 ((G'[t])^2) G''[t]+212430848 ((G[t])^2) H'[t] G''[t]+38083584 ((H[t])^2) H'[t] G''[t]-23747584 G'[t] H'[t] G''[t]+4153856 ((H'[t])^2) G''[t]-6651904 G[t] ((G''[t])^2)-35840 G[t] H[t] H'[t] (3649 G''[t]-1570 H''[t])+373115904 ((G[t])^4) H''[t]-579783680 ((G[t])^3) H[t] H''[t]+146650112 ((G[t])^2) ((H[t])^2) H''[t]+60017664 G[t] ((H[t])^3) H''[t]+207972352 ((G[t])^2) G'[t] H''[t]-122343424 G[t] H[t] G'[t] H''[t]+34105344 ((H[t])^2) G'[t] H''[t]-15439872 ((G'[t])^2) H''[t]-176003072 ((G[t])^2) H'[t] H''[t]+15439872 G'[t] H'[t] H''[t]+13303808 G[t] G''[t] H''[t]-6651904 G[t] ((H''[t])^2)+51724288 ((G[t])^2) H[t] Derivative[3][G][t]-6651904 G[t] G'[t] Derivative[3][G][t]+6651904 G[t] H'[t] Derivative[3][G][t]+7168 ((G[t])^3) (-159790 ((G'[t])^2)+248327 G'[t] H'[t]-92069 ((H'[t])^2)-4072 (Derivative[3][G][t]-Derivative[3][H][t]))-3584 G[t] ((H[t])^2) (28565 ((G'[t])^2)+5502 G'[t] H'[t]-7971 ((H'[t])^2)+6288 (Derivative[3][G][t]-Derivative[3][H][t]))-51724288 ((G[t])^2) H[t] Derivative[3][H][t]+6651904 G[t] G'[t] Derivative[3][H][t]-6651904 G[t] H'[t] Derivative[3][H][t]))+χ[t] (((70875 G[t]+10125 H[t])/10125)+(1/10125)Γ (-377975808 ((G[t])^7)+3071591936 ((G[t])^6) H[t]-8489908224 ((G[t])^5) ((H[t])^2)+10841750528 ((G[t])^4) ((H[t])^3)-6560762880 ((G[t])^3) ((H[t])^4)+1429804544 ((G[t])^2) ((H[t])^5)+121497600 G[t] ((H[t])^6)-35997696 ((H[t])^7)+326043648 ((H[t])^5) G'[t]+10404352 ((H[t])^3) ((G'[t])^2)+49032704 G[t] ((G'[t])^3)-113512448 H[t] ((G'[t])^3)+10752 ((G[t])^2) ((H[t])^3) (492110 G'[t]-491531 H'[t])-7168 G[t] ((H[t])^4) (383105 G'[t]-321631 H'[t])-148098048 ((H[t])^5) H'[t]-334702592 ((H[t])^3) G'[t] H'[t]-126465024 G[t] ((G'[t])^2) H'[t]+338827776 H[t] ((G'[t])^2) H'[t]+324025856 ((H[t])^3) ((H'[t])^2)-339641344 H[t] G'[t] ((H'[t])^2)-30922752 G[t] ((H'[t])^3)+114326016 H[t] ((H'[t])^3)+3584 ((G[t])^4) H[t] (-319012 G'[t]+67085 H'[t])-3584 ((G[t])^5) (-280415 G'[t]+202056 H'[t])+3584 ((G[t])^3) ((H[t])^2) (-762495 G'[t]+1007624 H'[t])+394171904 ((G[t])^4) G''[t]-1055674368 ((G[t])^3) H[t] G''[t]+876485120 ((G[t])^2) ((H[t])^2) G''[t]-72532992 ((H[t])^4) G''[t]+244400128 ((G[t])^2) G'[t] G''[t]+183335936 ((H[t])^2) G'[t] G''[t]-19593728 ((G'[t])^2) G''[t]-177673216 ((H[t])^2) H'[t] G''[t]+41710592 G'[t] H'[t] G''[t]-22116864 ((H'[t])^2) G''[t]+6651904 G[t] ((G''[t])^2)-5390336 H[t] ((G''[t])^2)-7168 G[t] ((H[t])^3) (19873 G''[t]-8423 H''[t])-371556864 ((G[t])^4) H''[t]+969271296 ((G[t])^3) H[t] H''[t]-751073792 ((G[t])^2) ((H[t])^2) H''[t]+92983296 ((H[t])^4) H''[t]-239045632 ((G[t])^2) G'[t] H''[t]-180504576 ((H[t])^2) G'[t] H''[t]+20224512 ((G'[t])^2) H''[t]+174841856 ((H[t])^2) H'[t] H''[t]-42972160 G'[t] H'[t] H''[t]+22747648 ((H'[t])^2) H''[t]-13303808 G[t] G''[t] H''[t]+10780672 H[t] G''[t] H''[t]+6651904 G[t] ((H''[t])^2)-5390336 H[t] ((H''[t])^2)+7168 ((G[t])^2) H'[t] (-32602 G''[t]+31855 H''[t])-7168 G[t] H[t] (G'[t] (56505 G''[t]-55363 H''[t])+H'[t] (-54221 G''[t]+53079 H''[t]))-25095168 ((H[t])^3) Derivative[3][G][t]-5390336 H[t] G'[t] Derivative[3][G][t]-6651904 G[t] H'[t] Derivative[3][G][t]+5390336 H[t] H'[t] Derivative[3][G][t]+3584 ((G[t])^2) H[t] (-615623 ((G'[t])^2)+947880 G'[t] H'[t]-334597 ((H'[t])^2)-22938 (Derivative[3][G][t]-Derivative[3][H][t]))+3584 G[t] G'[t] (30233 ((H'[t])^2)+1856 (Derivative[3][G][t]-Derivative[3][H][t]))+14336 ((G[t])^3) (79895 ((G'[t])^2)-133425 G'[t] H'[t]+53813 ((H'[t])^2)+2036 (Derivative[3][G][t]-Derivative[3][H][t]))+14336 G[t] ((H[t])^2) (77157 ((G'[t])^2)-87942 G'[t] H'[t]+11106 ((H'[t])^2)+5449 (Derivative[3][G][t]-Derivative[3][H][t]))+25095168 ((H[t])^3) Derivative[3][H][t]+5390336 H[t] G'[t] Derivative[3][H][t]+6651904 G[t] H'[t] Derivative[3][H][t]-5390336 H[t] H'[t] Derivative[3][H][t]))+Ψ[t] (-H[t]+(1/10125)Γ (-587776 ((G[t])^6) H[t]+1699134976 ((G[t])^5) ((H[t])^2)-5118529024 ((G[t])^4) ((H[t])^3)+5281586688 ((G[t])^3) ((H[t])^4)-1965189632 ((G[t])^2) ((H[t])^5)+67587072 G[t] ((H[t])^6)+35997696 ((H[t])^7)+1706747392 ((G[t])^4) H[t] G'[t]-347074560 ((H[t])^5) G'[t]+146273792 ((H[t])^3) ((G'[t])^2)+52437504 H[t] ((G'[t])^3)+7168 G[t] ((H[t])^4) (254543 G'[t]-250657 H'[t])-10913280 ((G[t])^5) H'[t]-1072866816 ((G[t])^4) H[t] H'[t]+148098048 ((H[t])^5) H'[t]+132772864 ((G[t])^3) G'[t] H'[t]+143919104 ((H[t])^3) G'[t] H'[t]-12045824 G[t] ((G'[t])^2) H'[t]-201238016 H[t] ((G'[t])^2) H'[t]-111512576 ((G[t])^3) ((H'[t])^2)-324025856 ((H[t])^3) ((H'[t])^2)+6128640 G[t] G'[t] ((H'[t])^2)+263126528 H[t] G'[t] ((H'[t])^2)+5917184 G[t] ((H'[t])^3)-114326016 H[t] ((H'[t])^3)+3584 ((G[t])^3) ((H[t])^2) (-530236 G'[t]+82379 H'[t])+3584 ((G[t])^2) ((H[t])^3) (-358223 G'[t]+680007 H'[t])+457282560 ((G[t])^3) H[t] G''[t]-797848576 ((G[t])^2) ((H[t])^2) G''[t]+310094848 G[t] ((H[t])^3) G''[t]+30471168 ((H[t])^4) G''[t]-111147008 ((H[t])^2) G'[t] G''[t]+21260288 ((G[t])^2) H'[t] G''[t]+139589632 ((H[t])^2) H'[t] G''[t]-17963008 G'[t] H'[t] G''[t]+17963008 ((H'[t])^2) G''[t]+5390336 H[t] ((G''[t])^2)-7168 G[t] H[t] H'[t] (35976 G''[t]-45229 H''[t])+7168 G[t] H[t] G'[t] (29042 G''[t]-38295 H''[t])-1559040 ((G[t])^4) H''[t]-389487616 ((G[t])^3) H[t] H''[t]+604423680 ((G[t])^2) ((H[t])^2) H''[t]-120393728 G[t] ((H[t])^3) H''[t]-92983296 ((H[t])^4) H''[t]+31073280 ((G[t])^2) G'[t] H''[t]+146399232 ((H[t])^2) G'[t] H''[t]-4784640 ((G'[t])^2) H''[t]-52333568 ((G[t])^2) H'[t] H''[t]-174841856 ((H[t])^2) H'[t] H''[t]+27532288 G'[t] H'[t] H''[t]-22747648 ((H'[t])^2) H''[t]-10780672 H[t] G''[t] H''[t]+5390336 H[t] ((H''[t])^2)+25095168 ((H[t])^3) Derivative[3][G][t]+5390336 H[t] G'[t] Derivative[3][G][t]-5390336 H[t] H'[t] Derivative[3][G][t]+3584 ((G[t])^2) H[t] (305426 ((G'[t])^2)-566824 G'[t] H'[t]+240094 ((H'[t])^2)+8506 (Derivative[3][G][t]-Derivative[3][H][t]))-3584 G[t] ((H[t])^2) (280063 ((G'[t])^2)-357270 G'[t] H'[t]+52395 ((H'[t])^2)+15508 (Derivative[3][G][t]-Derivative[3][H][t]))-25095168 ((H[t])^3) Derivative[3][H][t]-5390336 H[t] G'[t] Derivative[3][H][t]+5390336 H[t] H'[t] Derivative[3][H][t]))+α[t] (-1+(1/10125)Γ (-379151360 ((G[t])^6)+1381126656 ((G[t])^5) H[t]+99090432 ((H[t])^6)+2261504 ((G'[t])^3)-3584 ((G[t])^4) (488987 ((H[t])^2)+165177 G'[t]-144335 H'[t])-21504 ((H[t])^4) (10309 G'[t]-9454 H'[t])+154112 ((G'[t])^2) H'[t]-7092736 G'[t] ((H'[t])^2)+4677120 ((H'[t])^3)+1261568 ((G''[t])^2)+21504 ((H[t])^3) (326 G''[t]-207 H''[t])-2523136 G''[t] H''[t]+1261568 ((H''[t])^2)+3584 ((G[t])^3) (194915 ((H[t])^3)+8 H[t] (61251 G'[t]-51980 H'[t])-15340 G''[t]+14978 H''[t])+57344 H[t] (G'[t] (609 G''[t]-631 H''[t])+H'[t] (-653 G''[t]+675 H''[t]))+1261568 G'[t] Derivative[3][G][t]-1261568 H'[t] Derivative[3][G][t]-3584 G[t] (105438 ((H[t])^5)+((H[t])^3) (-258370 G'[t]+215626 H'[t])+((H[t])^2) (24884 G''[t]-23094 H''[t])+16 (G'[t] (213 G''[t]-235 H''[t])+H'[t] (-257 G''[t]+279 H''[t]))+H[t] (-42123 ((G'[t])^2)+63210 G'[t] H'[t]-20383 ((H'[t])^2)-1076 (Derivative[3][G][t]-Derivative[3][H][t])))+3584 ((H[t])^2) (1691 ((G'[t])^2)-18476 G'[t] H'[t]+17137 ((H'[t])^2)-714 (Derivative[3][G][t]-Derivative[3][H][t]))-1261568 G'[t] Derivative[3][H][t]+1261568 H'[t] Derivative[3][H][t]+3584 ((G[t])^2) (92293 ((H[t])^4)-28326 ((G'[t])^2)+50710 G'[t] H'[t]-22032 ((H'[t])^2)+((H[t])^2) (-521347 G'[t]+430407 H'[t])+H[t] (38268 G''[t]-36830 H''[t])-362 Derivative[3][G][t]+362 Derivative[3][H][t])))+(1/10125)Γ (6573056 ((G[t])^4)-24994816 ((G[t])^3) H[t]+34915328 ((G[t])^2) ((H[t])^2)-21138432 G[t] ((H[t])^3)+4644864 ((H[t])^4)+1297408 ((G[t])^2) G'[t]-3856384 G[t] H[t] G'[t]+2558976 ((H[t])^2) G'[t]-630784 ((G'[t])^2)-1297408 ((G[t])^2) H'[t]+3856384 G[t] H[t] H'[t]-2558976 ((H[t])^2) H'[t]+1261568 G'[t] H'[t]-630784 ((H'[t])^2)) Derivative[3][χ][t])-(1/3375)14336 Γ (6559 ((G[t])^5) H[t]+2934 ((H[t])^6)+((G[t])^3) H[t] (21346 ((H[t])^2)+8235 G'[t]-13808 H'[t])-2 ((G[t])^4) (9469 ((H[t])^2)-937 H'[t])-2679 ((H[t])^4) (2 G'[t]-3 H'[t])+1364 (((G'[t]-H'[t]))^2) H'[t]+((H[t])^2) (2128 ((G'[t])^2)-7066 G'[t] H'[t]+4938 ((H'[t])^2))+G[t] H[t] (-2721 ((H[t])^4)+((H[t])^2) (3947 G'[t]-11130 H'[t])+8 (757 ((G'[t])^2)-1323 G'[t] H'[t]+566 ((H'[t])^2))+82 H[t] (G''[t]-H''[t]))+((G[t])^2) (-9180 ((H[t])^4)+1282 (G'[t]-H'[t]) H'[t]+((H[t])^2) (-6824 G'[t]+15027 H'[t])+641 H[t] (G''[t]-H''[t]))-723 ((H[t])^3) (G''[t]-H''[t])+1364 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])) Derivative[3][Ψ][t]+(1/3375)7168 Γ (14055 ((G[t])^6)-41920 ((G[t])^5) H[t]+4 G'[t] (978 ((H[t])^4)-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2))+((G[t])^4) (50180 ((H[t])^2)+20859 G'[t]-15829 H'[t])+((G[t])^3) (-25930 ((H[t])^3)+H[t] (-26635 G'[t]+13089 H'[t])+1282 (G''[t]-H''[t]))+((G[t])^2) (-1275 ((H[t])^4)+((H[t])^2) (24613 G'[t]-8699 H'[t])+14 (1097 ((G'[t])^2)-1816 G'[t] H'[t]+719 ((H'[t])^2))+164 H[t] (G''[t]-H''[t]))+G[t] (4890 ((H[t])^5)-3 ((H[t])^3) (7583 G'[t]-3813 H'[t])+2 H[t] (1951 ((G'[t])^2)-5102 G'[t] H'[t]+3151 ((H'[t])^2))-1446 ((H[t])^2) (G''[t]-H''[t])+2728 (G'[t]-H'[t]) (G''[t]-H''[t]))) Derivative[3][(OverBar[Ψ])][t]+(OverBar[Ψ])[t] (-((7 (27000 G[t] G'[t]+6750 H[t] G'[t]+3375 G''[t]))/3375)-(1/3375)7 Γ (167936 ((G[t])^7) G'[t]-58936320 G[t] ((H[t])^6) G'[t]+21012480 ((H[t])^7) G'[t]-58809344 G[t] ((G'[t])^4)-2752512 H[t] ((G'[t])^4)-2048 G[t] ((G'[t])^3) (79853 ((H[t])^2)-69827 H'[t])-479416320 G[t] ((H[t])^4) G'[t] H'[t]+16538624 H[t] ((G'[t])^3) H'[t]+28180480 G[t] G'[t] ((H'[t])^3)+8240128 H[t] G'[t] ((H'[t])^3)+2995200 ((H[t])^6) G''[t]-21602304 ((G'[t])^3) G''[t]+38436864 ((G'[t])^2) H'[t] G''[t]-14860288 G'[t] ((H'[t])^2) G''[t]-1974272 ((H'[t])^3) G''[t]-27514880 G[t] G'[t] ((G''[t])^2)-7403520 H[t] G'[t] ((G''[t])^2)-1396736 ((G''[t])^3)-512 ((G[t])^6) (738626 H[t] G'[t]+104903 G''[t])+24576 G[t] ((H[t])^3) G'[t] (5513 G''[t]-1530 H''[t])+12402688 ((G'[t])^3) H''[t]-22011904 ((G'[t])^2) H'[t] H''[t]+9609216 G'[t] ((H'[t])^2) H''[t]+27430912 G[t] G'[t] G''[t] H''[t]+8884224 H[t] G'[t] G''[t] H''[t]+2793472 ((G''[t])^2) H''[t]-1312768 G[t] G'[t] ((H''[t])^2)-83968 H[t] G'[t] ((H''[t])^2)-1396736 G''[t] ((H''[t])^2)+1024 ((G[t])^5) (1386711 ((H[t])^2) G'[t]-314709 ((G'[t])^2)+230256 G'[t] H'[t]+95975 H[t] G''[t]-14055 Derivative[3][G][t])-4190208 G'[t] G''[t] Derivative[3][G][t]+4190208 H'[t] G''[t] Derivative[3][G][t]+2793472 G'[t] H''[t] Derivative[3][G][t]-2793472 H'[t] H''[t] Derivative[3][G][t]-3072 ((H[t])^5) (30177 ((G'[t])^2)-22689 G'[t] H'[t]+1630 Derivative[3][G][t])-2048 H[t] H'[t] (-4938 ((G''[t])^2)+5620 G''[t] H''[t]+3151 H'[t] Derivative[3][G][t])-1024 G[t] ((H[t])^2) G'[t] (56406 ((H'[t])^2)+15851 Derivative[3][G][t]-8762 Derivative[3][H][t])+2048 G[t] G'[t] H'[t] (12071 Derivative[3][G][t]-641 Derivative[3][H][t])-2048 H[t] ((G'[t])^2) (10755 ((H'[t])^2)+1828 Derivative[3][G][t]-41 Derivative[3][H][t])+2048 H[t] G'[t] H'[t] (4979 Derivative[3][G][t]-41 Derivative[3][H][t])+1396736 G'[t] G''[t] Derivative[3][H][t]-1396736 H'[t] G''[t] Derivative[3][H][t]+1024 G[t] ((G'[t])^2) (482169 ((H[t])^4)+216604 ((H[t])^2) H'[t]-109743 ((H'[t])^2)+H[t] (20350 G''[t]-27296 H''[t])-14076 Derivative[3][G][t]+1282 Derivative[3][H][t])+1024 ((H[t])^3) (40226 ((G'[t])^3)-40242 ((G'[t])^2) H'[t]-3 (-3331 ((G''[t])^2)+3572 G''[t] H''[t]+3813 H'[t] Derivative[3][G][t])-3 G'[t] (504 ((H'[t])^2)-4394 Derivative[3][G][t]+1063 Derivative[3][H][t]))+3072 ((H[t])^4) (-10503 H'[t] G''[t]+2 G'[t] (2537 G''[t]-907 H''[t])-326 Derivative[4][G][t])+2048 G[t] H[t] G'[t] (2 H'[t] (1531 G''[t]+6265 H''[t])-41 Derivative[4][G][t])-698368 ((G'[t])^2) Derivative[4][G][t]+1396736 G'[t] H'[t] Derivative[4][G][t]-698368 ((H'[t])^2) Derivative[4][G][t]-1024 ((G[t])^4) (2011280 ((H[t])^3) G'[t]-34202 ((H[t])^2) G''[t]-110611 H'[t] G''[t]+G'[t] (204556 G''[t]-65590 H''[t])-5 H[t] (95975 ((G'[t])^2)-43625 G'[t] H'[t]+8384 Derivative[3][G][t])+937 Derivative[4][G][t])+1024 ((G[t])^3) (1322344 ((H[t])^4) G'[t]-268562 ((G'[t])^3)+442444 ((G'[t])^2) H'[t]-231204 ((H[t])^3) G''[t]-17111 ((G''[t])^2)+16470 G''[t] H''[t]+4 ((H[t])^2) (34202 ((G'[t])^2)-109472 G'[t] H'[t]-12545 Derivative[3][G][t])+15829 H'[t] Derivative[3][G][t]+G'[t] (-176446 ((H'[t])^2)-20859 Derivative[3][G][t]+3748 Derivative[3][H][t])+H[t] (-147162 H'[t] G''[t]+68 G'[t] (5401 G''[t]-2228 H''[t])+3107 Derivative[4][G][t]))-512 ((G[t])^2) (583182 ((H[t])^5) G'[t]-482169 ((H[t])^4) G''[t]+109743 ((H'[t])^2) G''[t]+9 ((G'[t])^2) (30551 G''[t]-10980 H''[t])+4 ((H[t])^3) (346806 ((G'[t])^2)-412935 G'[t] H'[t]-12965 Derivative[3][G][t])+3846 G''[t] Derivative[3][G][t]-2564 H''[t] Derivative[3][G][t]+H[t] (-598764 ((G'[t])^3)+882972 ((G'[t])^2) H'[t]-28414 ((G''[t])^2)+27296 G''[t] H''[t]+26178 H'[t] Derivative[3][G][t]-2 G'[t] (145704 ((H'[t])^2)+23528 Derivative[3][G][t]-9321 Derivative[3][H][t]))-1282 G''[t] Derivative[3][H][t]-1282 H'[t] Derivative[4][G][t]+G'[t] (H'[t] (-374282 G''[t]+91128 H''[t])+1282 Derivative[4][G][t])+((H[t])^2) (-216604 H'[t] G''[t]+4 G'[t] (155123 G''[t]-64038 H''[t])+8762 Derivative[4][G][t]))-1024 G[t] (90531 ((H[t])^5) G''[t]-1275 ((H[t])^4) Derivative[3][G][t]+((H[t])^2) (7089 ((G''[t])^2)-7894 G''[t] H''[t]-8699 H'[t] Derivative[3][G][t])+2 H'[t] (-11430 ((G''[t])^2)+10748 G''[t] H''[t]+5033 H'[t] Derivative[3][G][t])+((H[t])^3) (40242 H'[t] G''[t]-3189 Derivative[4][G][t])+2 H[t] (10755 ((H'[t])^2) G''[t]-82 H''[t] Derivative[3][G][t]+41 G''[t] (3 Derivative[3][G][t]-Derivative[3][H][t])-41 H'[t] Derivative[4][G][t]))-512 ((H[t])^2) (((G'[t])^2) (34449 G''[t]-15788 H''[t])-6 G'[t] (H'[t] (15145 G''[t]-3168 H''[t])+241 Derivative[4][G][t])+3 (18643 ((H'[t])^2) G''[t]+482 (2 H''[t] Derivative[3][G][t]+G''[t] (-3 Derivative[3][G][t]+Derivative[3][H][t]))+482 H'[t] Derivative[4][G][t]))))+Ψ[t] (((2 (-23625 G[t] H'[t]-10125 H[t] H'[t]-3375 H''[t]))/3375)+(1/3375)2 Γ (189088256 ((G[t])^7) H'[t]-514805760 G[t] ((H[t])^6) H'[t]+35997696 ((H[t])^7) H'[t]+1622315520 G[t] ((H[t])^4) G'[t] H'[t]+9633792 G[t] ((G'[t])^3) H'[t]+24217088 H[t] ((G'[t])^3) H'[t]+200449536 H[t] G'[t] ((H'[t])^3)+64512 G[t] (252 ((H[t])^2)+1195 G'[t]) ((H'[t])^3)-28840448 G[t] ((H'[t])^4)-93004800 H[t] ((H'[t])^4)+12809216 ((G'[t])^2) H'[t] G''[t]-35395584 G'[t] ((H'[t])^2) G''[t]+22586368 ((H'[t])^3) G''[t]+293888 G[t] H'[t] ((G''[t])^2)-5182464 H[t] H'[t] ((G''[t])^2)-43008 G[t] ((H[t])^3) H'[t] (425 G''[t]-2066 H''[t])-19547136 ((H[t])^6) H''[t]-17532928 ((G'[t])^3) H''[t]+680960 ((G'[t])^2) H'[t] H''[t]+61014016 G'[t] ((H'[t])^2) H''[t]-44162048 ((H'[t])^3) H''[t]+71565312 G[t] H'[t] G''[t] H''[t]+55537664 H[t] H'[t] G''[t] H''[t]-4888576 ((G''[t])^2) H''[t]-66970624 G[t] H'[t] ((H''[t])^2)-55243776 H[t] H'[t] ((H''[t])^2)+9777152 G''[t] ((H''[t])^2)-4888576 ((H''[t])^3)-10752 ((G[t])^6) (154079 H[t] H'[t]+12792 H''[t])-4888576 G'[t] H''[t] Derivative[3][G][t]+4888576 H'[t] H''[t] Derivative[3][G][t]+3584 ((G[t])^5) (1206768 ((H[t])^2) H'[t]-95975 G'[t] H'[t]+43625 ((H'[t])^2)+43625 H[t] H''[t]-13118 Derivative[3][H][t])-10752 G[t] ((H[t])^2) H'[t] (40226 ((G'[t])^2)+3189 Derivative[3][G][t]-6357 Derivative[3][H][t])-7168 H[t] G'[t] H'[t] (723 Derivative[3][G][t]-6343 Derivative[3][H][t])-9777152 G'[t] G''[t] Derivative[3][H][t]+9777152 H'[t] G''[t] Derivative[3][H][t]+14665728 G'[t] H''[t] Derivative[3][H][t]-14665728 H'[t] H''[t] Derivative[3][H][t]-64512 ((H[t])^5) (975 G'[t] H'[t]+1818 ((H'[t])^2)+326 Derivative[3][H][t])-7168 H[t] ((H'[t])^2) (18368 ((G'[t])^2)-723 Derivative[3][G][t]+4215 Derivative[3][H][t])-3584 G[t] ((H'[t])^2) (340335 ((H[t])^4)-120726 ((H[t])^2) G'[t]+16151 ((G'[t])^2)+H[t] (17398 G''[t]+5133 H''[t])+82 Derivative[3][G][t]+9302 Derivative[3][H][t])+7168 G[t] G'[t] H'[t] (41 Derivative[3][G][t]+10707 Derivative[3][H][t])-14336 H[t] G'[t] (2469 G''[t] H''[t]-2810 ((H''[t])^2)+1064 G'[t] Derivative[3][H][t])-10752 ((H[t])^3) (9298 ((G'[t])^2) H'[t]+33678 ((H'[t])^3)+H''[t] (-3813 G''[t]+4054 H''[t])-4 G'[t] (10503 ((H'[t])^2)+893 Derivative[3][H][t])+H'[t] (-1304 Derivative[3][G][t]+5358 Derivative[3][H][t]))+10752 ((H[t])^4) (H'[t] (8150 G''[t]-26619 H''[t])+10503 G'[t] H''[t]-326 Derivative[4][H][t])-2444288 ((G'[t])^2) Derivative[4][H][t]+4888576 G'[t] H'[t] Derivative[4][H][t]-2444288 ((H'[t])^2) Derivative[4][H][t]+7168 G[t] H[t] H'[t] (G'[t] (7089 G''[t]+13616 H''[t])+41 Derivative[4][H][t])-3584 ((G[t])^4) (1322344 ((H[t])^3) H'[t]+H'[t] (41920 G''[t]-126099 H''[t])-109472 ((H[t])^2) H''[t]+110611 G'[t] H''[t]+4 H[t] (17101 G'[t] H'[t]-54736 ((H'[t])^2)-9469 Derivative[3][H][t])+937 Derivative[4][H][t])-3584 ((H[t])^2) (18368 ((G'[t])^2) H''[t]+((H'[t])^2) (-34317 G''[t]+75411 H''[t])-723 (H''[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+2 G''[t] Derivative[3][H][t])+3 G'[t] (H'[t] (9993 G''[t]-29359 H''[t])-241 Derivative[4][H][t])+723 H'[t] Derivative[4][H][t])+3584 ((G[t])^3) (485985 ((H[t])^4) H'[t]-99794 ((G'[t])^2) H'[t]-48568 ((H'[t])^3)-275290 ((H[t])^3) H''[t]-15829 G''[t] H''[t]+15188 ((H''[t])^2)-3107 H'[t] Derivative[3][G][t]+((H[t])^2) (693612 G'[t] H'[t]-825870 ((H'[t])^2)-42692 Derivative[3][H][t])+6 G'[t] (24527 ((H'[t])^2)-2745 Derivative[3][H][t])+18295 H'[t] Derivative[3][H][t]+H[t] (520 H'[t] (193 G''[t]-351 H''[t])+147162 G'[t] H''[t]+3107 Derivative[4][H][t]))+3584 ((G[t])^2) (172665 ((H[t])^5) H'[t]+13089 ((H'[t])^2) G''[t]+234090 ((H[t])^4) H''[t]-69827 ((G'[t])^2) H''[t]-53810 ((H'[t])^2) H''[t]-641 H''[t] Derivative[3][G][t]+H[t] (159706 ((G'[t])^2) H'[t]+56406 ((H'[t])^3)+(13089 G''[t]-12530 H''[t]) H''[t]+H'[t] (8762 Derivative[3][G][t]-21292 Derivative[3][H][t])-4 G'[t] (54151 ((H'[t])^2)-3412 Derivative[3][H][t]))-1282 G''[t] Derivative[3][H][t]+1923 H''[t] Derivative[3][H][t]+((H[t])^3) (-964338 G'[t] H'[t]+18360 (51 ((H'[t])^2)+Derivative[3][H][t]))+G'[t] (H'[t] (-14207 G''[t]+123391 H''[t])-641 Derivative[4][H][t])+641 H'[t] Derivative[4][H][t]-((H[t])^2) (6 H'[t] (12965 G''[t]-18581 H''[t])+108302 G'[t] H''[t]+4381 Derivative[4][H][t]))-3584 G[t] (68067 ((H[t])^5) H''[t]-5442 ((H[t])^4) Derivative[3][H][t]+4 G'[t] (5715 G''[t] H''[t]-5374 ((H''[t])^2)+3028 G'[t] Derivative[3][H][t])+((H[t])^2) (8699 G''[t] H''[t]-9504 ((H''[t])^2)+7894 G'[t] Derivative[3][H][t])-3 ((H[t])^3) (13414 G'[t] H''[t]+1063 Derivative[4][H][t])+H[t] (16151 ((G'[t])^2) H''[t]+82 (H''[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+2 G''[t] Derivative[3][H][t])+82 G'[t] Derivative[4][H][t]))))-(1/3375)7168 Γ H[t] (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[4][Ψ][t]+(1/3375)7168 Γ G[t] (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[4][(OverBar[Ψ])][t];

(* E7Zero=eq.(39) *)

E7Zero=(1/((a[t])^4))(k^4) ((1/10125)1024 Γ α[t] (706 ((G[t])^4)-4001 ((G[t])^3) H[t]+8818 ((G[t])^2) ((H[t])^2)-8457 G[t] ((H[t])^3)+2934 ((H[t])^4)-1177 ((G[t])^2) (G'[t]-H'[t])+4456 G[t] H[t] (G'[t]-H'[t])-3279 ((H[t])^2) (G'[t]-H'[t])+1051 (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ (OverBar[Ψ])[t] (-2603 ((G[t])^5)+13243 ((G[t])^4) H[t]-27479 ((G[t])^3) ((H[t])^2)+25641 ((G[t])^2) ((H[t])^3)-8802 G[t] ((H[t])^4)+2831 ((G[t])^3) (G'[t]-H'[t])-12398 ((G[t])^2) H[t] (G'[t]-H'[t])+9567 G[t] ((H[t])^2) (G'[t]-H'[t])-3368 G[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ χ[t] (2603 ((G[t])^5)-15140 ((G[t])^4) H[t]+36721 ((G[t])^3) ((H[t])^2)-44302 ((G[t])^2) ((H[t])^3)+25986 G[t] ((H[t])^4)-5868 ((H[t])^5)-2831 ((G[t])^3) (G'[t]-H'[t])+14052 ((G[t])^2) H[t] (G'[t]-H'[t])-17509 G[t] ((H[t])^2) (G'[t]-H'[t])+6288 ((H[t])^3) (G'[t]-H'[t])+3368 G[t] (((G'[t]-H'[t]))^2)-2317 H[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ Ψ[t] (1897 ((G[t])^4) H[t]-9242 ((G[t])^3) ((H[t])^2)+18661 ((G[t])^2) ((H[t])^3)-17184 G[t] ((H[t])^4)+5868 ((H[t])^5)-1654 ((G[t])^2) H[t] (G'[t]-H'[t])+7942 G[t] ((H[t])^2) (G'[t]-H'[t])-6288 ((H[t])^3) (G'[t]-H'[t])+2317 H[t] (((G'[t]-H'[t]))^2))+(1/10125)1024 Γ (-706 ((G[t])^4)+4001 ((G[t])^3) H[t]-8818 ((G[t])^2) ((H[t])^2)+8457 G[t] ((H[t])^3)-2934 ((H[t])^4)+1177 ((G[t])^2) (G'[t]-H'[t])-4456 G[t] H[t] (G'[t]-H'[t])+3279 ((H[t])^2) (G'[t]-H'[t])-1051 (((G'[t]-H'[t]))^2)) χ'[t])+(1/1125)1024 Γ (13118 ((G[t])^6)-50057 ((G[t])^5) H[t]-6846 ((H[t])^6)+2 ((G[t])^4) (38262 ((H[t])^2)+10109 G'[t]-9468 H'[t])+3 ((H[t])^4) (5117 G'[t]-5599 H'[t])+2728 (((G'[t]-H'[t]))^3)-2 ((H[t])^2) (3915 ((G'[t])^2)-9194 G'[t] H'[t]+5279 ((H'[t])^2))+((G[t])^3) (-53564 ((H[t])^3)-5 H[t] (8381 G'[t]-7901 H'[t])+1282 (G''[t]-H''[t]))+((G[t])^2) (5348 ((H[t])^4)+((H[t])^2) (38507 G'[t]-38999 H'[t])+4 (3669 ((G'[t])^2)-6656 G'[t] H'[t]+2987 ((H'[t])^2))-1118 H[t] (G''[t]-H''[t]))+G[t] (15477 ((H[t])^5)+((H[t])^3) (-32171 G'[t]+35227 H'[t])-2 H[t] (3423 ((G'[t])^2)-4118 G'[t] H'[t]+695 ((H'[t])^2))-1610 ((H[t])^2) (G''[t]-H''[t])+2728 (G'[t]-H'[t]) (G''[t]-H''[t]))+1446 ((H[t])^3) (G''[t]-H''[t])-2728 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])) α''[t]+α[t] (((2 (23625 ((G[t])^2)+20250 G[t] H[t]+6750 ((H[t])^2)+6750 G'[t]+3375 H'[t]))/1125)+(1/1125)2 Γ (188563456 ((G[t])^7) H[t]+369512448 ((G[t])^2) ((H[t])^6)-150921216 G[t] ((H[t])^7)+11999232 ((H[t])^8)+111538176 ((G[t])^2) ((G'[t])^3)+17584128 G[t] H[t] ((G'[t])^3)+13344768 ((H[t])^2) ((G'[t])^3)+9897984 ((G'[t])^4)-2048 ((G[t])^2) ((H[t])^4) (558386 G'[t]-520923 H'[t])+12288 G[t] ((H[t])^5) (33725 G'[t]-24522 H'[t])-270563328 ((G[t])^2) ((G'[t])^2) H'[t]-80289792 G[t] H[t] ((G'[t])^2) H'[t]-76548096 ((H[t])^2) ((G'[t])^2) H'[t]-25624576 ((G'[t])^3) H'[t]+17485824 ((G'[t])^2) ((H'[t])^2)-53073920 ((G[t])^2) ((H'[t])^3)-33947648 G[t] H[t] ((H'[t])^3)-55445504 ((H[t])^2) ((H'[t])^3)+2310144 G'[t] ((H'[t])^3)-4069376 ((H'[t])^4)-12288 ((H[t])^6) (1160 G'[t]+1959 H'[t])-2048 ((G[t])^6) (383120 ((H[t])^2)-91826 G'[t]+65549 H'[t])+2625536 ((G[t])^2) ((G''[t])^2)+335872 G[t] H[t] ((G''[t])^2)-2961408 ((H[t])^2) ((G''[t])^2)+5586944 G'[t] ((G''[t])^2)-5586944 H'[t] ((G''[t])^2)+4096 ((G[t])^5) (301212 ((H[t])^3)+H[t] (-66853 G'[t]+19484 H'[t])+937 (14 G''[t]-13 H''[t]))-12288 G[t] ((H[t])^4) (1814 G''[t]-3203 H''[t])-40960 ((G[t])^2) ((H[t])^3) (1836 G''[t]-1079 H''[t])+4005888 ((H[t])^5) (6 G''[t]-7 H''[t])-5251072 ((G[t])^2) G''[t] H''[t]-671744 G[t] H[t] G''[t] H''[t]+5922816 ((H[t])^2) G''[t] H''[t]-11173888 G'[t] G''[t] H''[t]+11173888 H'[t] G''[t] H''[t]+2625536 ((G[t])^2) ((H''[t])^2)+335872 G[t] H[t] ((H''[t])^2)-2961408 ((H[t])^2) ((H''[t])^2)+5586944 G'[t] ((H''[t])^2)-5586944 H'[t] ((H''[t])^2)+8192 H[t] (G'[t]-H'[t]) (G'[t] (2128 G''[t]-2469 H''[t])+H'[t] (-3492 G''[t]+3833 H''[t]))-12288 ((H[t])^3) (G'[t] (3572 G''[t]-3813 H''[t])+H'[t] (-4054 G''[t]+4295 H''[t]))+8192 G[t] (G'[t]-H'[t]) (G'[t] (6056 G''[t]-5715 H''[t])+H'[t] (-4692 G''[t]+4351 H''[t]))+4096 G[t] ((H[t])^2) (G'[t] (7894 G''[t]-8699 H''[t])+H'[t] (-9504 G''[t]+10309 H''[t]))-4096 ((G[t])^2) H[t] (G'[t] (13648 G''[t]-13089 H''[t])+H'[t] (-12530 G''[t]+11971 H''[t]))+2793472 ((G'[t])^2) Derivative[3][G][t]-2625536 ((G[t])^2) H'[t] Derivative[3][G][t]-5586944 G'[t] H'[t] Derivative[3][G][t]+2793472 ((H'[t])^2) Derivative[3][G][t]-2048 ((G[t])^4) (373157 ((H[t])^4)+4 ((H[t])^2) (45658 G'[t]-77527 H'[t])+8 H[t] (9469 G''[t]-8458 H''[t])-2 (64897 ((G'[t])^2)-106765 G'[t] H'[t]+42509 ((H'[t])^2)+937 (Derivative[3][G][t]-Derivative[3][H][t])))-4096 ((G[t])^3) (25406 ((H[t])^5)-6 ((H[t])^3) (48959 G'[t]-53797 H'[t])+H'[t] (15188 G''[t]-14547 H''[t])-52 ((H[t])^2) (821 G''[t]-677 H''[t])+G'[t] (-16470 G''[t]+15829 H''[t])+H[t] (98158 ((G'[t])^2)-145090 G'[t] H'[t]+48132 ((H'[t])^2)+3107 (Derivative[3][G][t]-Derivative[3][H][t])))+4096 ((H[t])^2) G'[t] (28967 ((H'[t])^2)-723 (Derivative[3][G][t]-Derivative[3][H][t]))-12288 ((H[t])^4) (2445 ((G'[t])^2)-10985 G'[t] H'[t]+8781 ((H'[t])^2)-326 (Derivative[3][G][t]-Derivative[3][H][t]))+4096 G[t] H[t] G'[t] (23597 ((H'[t])^2)+82 (Derivative[3][G][t]-Derivative[3][H][t]))+4096 ((G[t])^2) G'[t] (51782 ((H'[t])^2)+641 (Derivative[3][G][t]-Derivative[3][H][t]))-4096 G[t] ((H[t])^3) (42354 ((G'[t])^2)-42970 G'[t] H'[t]-912 ((H'[t])^2)+3189 (Derivative[3][G][t]-Derivative[3][H][t]))+4096 ((G[t])^2) ((H[t])^2) (82950 ((G'[t])^2)-114250 G'[t] H'[t]+31054 ((H'[t])^2)+4381 (Derivative[3][G][t]-Derivative[3][H][t]))-335872 G[t] H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])+2961408 ((H[t])^2) H'[t] (Derivative[3][G][t]-Derivative[3][H][t])-2793472 ((G'[t])^2) Derivative[3][H][t]+2625536 ((G[t])^2) H'[t] Derivative[3][H][t]+5586944 G'[t] H'[t] Derivative[3][H][t]-2793472 ((H'[t])^2) Derivative[3][H][t]))+(OverBar[Ψ])''[t] (-6 G[t]-(1/1125)2 Γ (23507456 ((G[t])^7)-34228736 ((G[t])^6) H[t]-1781760 G[t] ((H[t])^6)+23553024 G[t] ((G'[t])^3)-1536 G[t] ((H[t])^4) (10332 G'[t]-10985 H'[t])-42627072 G[t] ((G'[t])^2) H'[t]+288768 G[t] ((H'[t])^3)-512 ((G[t])^5) (91316 ((H[t])^2)-169148 G'[t]+106765 H'[t])+698368 G[t] ((G''[t])^2)+512 ((G[t])^4) (293754 ((H[t])^3)+H[t] (-309944 G'[t]+145090 H'[t])+22092 G''[t]-15829 H''[t])-1536 G[t] ((H[t])^3) (9950 G''[t]-3813 H''[t])-1396736 G[t] G''[t] H''[t]+698368 G[t] ((H''[t])^2)+2048 G[t] H[t] (G'[t] (2374 G''[t]-2592 H''[t])+H'[t] (-2933 G''[t]+3151 H''[t]))+3072 (2934 ((H[t])^5) G'[t]+((H[t])^3) (-5358 ((G'[t])^2)+6081 G'[t] H'[t])+4 H[t] G'[t] (532 ((G'[t])^2)-1405 G'[t] H'[t]+873 ((H'[t])^2))+978 ((H[t])^4) G''[t]+682 (G'[t]-H'[t]) (-H'[t] G''[t]+G'[t] (3 G''[t]-2 H''[t]))+723 ((H[t])^2) (H'[t] G''[t]+G'[t] (-2 G''[t]+H''[t])))-698368 G[t] H'[t] Derivative[3][G][t]+512 ((G[t])^2) (101175 ((H[t])^5)+((H[t])^3) (-139788 G'[t]+42970 H'[t])+G'[t] (31916 G''[t]-26706 H''[t])+((H[t])^2) (34180 G''[t]-8699 H''[t])+2 H'[t] (-12671 G''[t]+10066 H''[t])+H[t] (-28065 ((G'[t])^2)-1614 G'[t] H'[t]+23597 ((H'[t])^2)+82 Derivative[3][G][t]-82 Derivative[3][H][t]))+1024 G[t] G'[t] (18345 ((H'[t])^2)+682 (Derivative[3][G][t]-Derivative[3][H][t]))+698368 G[t] H'[t] Derivative[3][H][t]-512 ((G[t])^3) (279193 ((H[t])^4)-131103 ((G'[t])^2)+177675 G'[t] H'[t]-51782 ((H'[t])^2)+((H[t])^2) (-293976 G'[t]+114250 H'[t])+H[t] (32290 G''[t]-13089 H''[t])-641 Derivative[3][G][t]+641 Derivative[3][H][t])+512 G[t] ((H[t])^2) (33456 ((G'[t])^2)-65889 G'[t] H'[t]+28967 ((H'[t])^2)-723 Derivative[3][G][t]+723 Derivative[3][H][t])))+Ψ'[t] (-((2 (10125 G[t] H[t]+6750 ((H[t])^2)+3375 H'[t]))/1125)-(1/1125)2 Γ (23570432 ((G[t])^7) H[t]-132056064 G[t] ((H[t])^7)+11999232 ((H[t])^8)+2198016 G[t] H[t] ((G'[t])^3)+3336192 ((H[t])^2) ((G'[t])^3)+1536 G[t] ((H[t])^5) (168625 G'[t]-171654 H'[t])-30108672 G[t] H[t] ((G'[t])^2) H'[t]-38274048 ((H[t])^2) ((G'[t])^2) H'[t]-6406144 ((G'[t])^3) H'[t]+8742912 ((G'[t])^2) ((H'[t])^2)-29704192 G[t] H[t] ((H'[t])^3)-55445504 ((H[t])^2) ((H'[t])^3)+1732608 G'[t] ((H'[t])^3)-4069376 ((H'[t])^4)-36864 ((H[t])^6) (290 G'[t]+653 H'[t])-512 ((G[t])^6) (383120 ((H[t])^2)+65549 H'[t])+41984 G[t] H[t] ((G''[t])^2)-740352 ((H[t])^2) ((G''[t])^2)-1396736 H'[t] ((G''[t])^2)+512 ((G[t])^5) (903636 ((H[t])^3)+H[t] (-66853 G'[t]+58452 H'[t])-36543 H''[t])-1536 G[t] ((H[t])^4) (7256 G''[t]-22421 H''[t])+1001472 ((H[t])^5) (15 G''[t]-28 H''[t])-335872 G[t] H[t] G''[t] H''[t]+3701760 ((H[t])^2) G''[t] H''[t]-4190208 G'[t] G''[t] H''[t]+6983680 H'[t] G''[t] H''[t]+293888 G[t] H[t] ((H''[t])^2)-2961408 ((H[t])^2) ((H''[t])^2)+4190208 G'[t] ((H''[t])^2)-5586944 H'[t] ((H''[t])^2)+4096 H[t] (((H'[t])^2) (4365 G''[t]-7666 H''[t])+((G'[t])^2) (532 G''[t]-2469 H''[t])+3 G'[t] H'[t] (-1405 G''[t]+3151 H''[t]))-3072 ((H[t])^3) (3 G'[t] (1786 G''[t]-3813 H''[t])+5 H'[t] (-2027 G''[t]+3436 H''[t]))-1024 G[t] (2 G'[t] H'[t] (10748 G''[t]-25165 H''[t])+17145 ((G'[t])^2) H''[t]+((H'[t])^2) (-18768 G''[t]+30457 H''[t]))+512 G[t] ((H[t])^2) (G'[t] (15788 G''[t]-43495 H''[t])+H'[t] (-38016 G''[t]+72163 H''[t]))-1396736 G'[t] H'[t] Derivative[3][G][t]+1396736 ((H'[t])^2) Derivative[3][G][t]-512 ((G[t])^3) (127030 ((H[t])^5)+((H[t])^3) (-881262 G'[t]+1613910 H'[t])+30376 H'[t] G''[t]-52 ((H[t])^2) (1642 G''[t]-3385 H''[t])+47487 G'[t] H''[t]-72735 H'[t] H''[t]+H[t] (98158 ((G'[t])^2)-435270 G'[t] H'[t]+240660 ((H'[t])^2)+3107 (Derivative[3][G][t]-5 Derivative[3][H][t])))-512 G[t] ((H[t])^3) (127062 ((G'[t])^2)-214850 G'[t] H'[t]-6384 ((H'[t])^2)+3189 (3 Derivative[3][G][t]-7 Derivative[3][H][t]))+512 G[t] H[t] G'[t] (117985 ((H'[t])^2)+82 (Derivative[3][G][t]-5 Derivative[3][H][t]))+3072 ((H[t])^2) G'[t] (28967 ((H'[t])^2)-241 (Derivative[3][G][t]-3 Derivative[3][H][t]))-3072 ((H[t])^4) (4890 ((G'[t])^2)-32955 G'[t] H'[t]+35124 ((H'[t])^2)-652 (Derivative[3][G][t]-2 Derivative[3][H][t]))-41984 G[t] H[t] H'[t] (3 Derivative[3][G][t]-7 Derivative[3][H][t])+1480704 ((H[t])^2) H'[t] (Derivative[3][G][t]-2 Derivative[3][H][t])-1396736 ((G'[t])^2) Derivative[3][H][t]+4190208 G'[t] H'[t] Derivative[3][H][t]-2793472 ((H'[t])^2) Derivative[3][H][t]-1024 ((G[t])^4) (373157 ((H[t])^4)+4 ((H[t])^2) (22829 G'[t]-77527 H'[t])+106765 G'[t] H'[t]-85018 ((H'[t])^2)+2 H[t] (9469 G''[t]-33832 H''[t])+1874 Derivative[3][H][t])+512 ((G[t])^2) (541278 ((H[t])^6)-132111 ((G'[t])^2) H'[t]-77745 ((H'[t])^3)+((H[t])^4) (-1116772 G'[t]+1562769 H'[t])-60 ((H[t])^3) (918 G''[t]-1079 H''[t])-3846 G''[t] H''[t]+3846 ((H''[t])^2)+H[t] (6 H'[t] (6265 G''[t]-11971 H''[t])+G'[t] (-13648 G''[t]+52356 H''[t]))-1282 H'[t] Derivative[3][G][t]+2 ((H[t])^2) (82950 ((G'[t])^2)-228500 G'[t] H'[t]+93162 ((H'[t])^2)+4381 (Derivative[3][G][t]-3 Derivative[3][H][t]))+4 G'[t] (51782 ((H'[t])^2)-641 Derivative[3][H][t])+3846 H'[t] Derivative[3][H][t])))+(OverBar[Ψ])'[t] (-((2 (23625 ((G[t])^2)+10125 G[t] H[t]+6750 G'[t]))/1125)-(1/1125)2 Γ (164993024 ((G[t])^7) H[t]+92378112 ((G[t])^2) ((H[t])^6)-18865152 G[t] ((H[t])^7)-3563520 ((H[t])^6) G'[t]+111538176 ((G[t])^2) ((G'[t])^3)+15386112 G[t] H[t] ((G'[t])^3)+9897984 ((G'[t])^4)-512 ((G[t])^2) ((H[t])^4) (1116772 G'[t]-520923 H'[t])+4608 G[t] ((H[t])^5) (33725 G'[t]-8174 H'[t])+6144 ((G'[t])^3) (1629 ((H[t])^2)-3128 H'[t])+33745920 ((H[t])^4) G'[t] H'[t]-202922496 ((G[t])^2) ((G'[t])^2) H'[t]-50181120 G[t] H[t] ((G'[t])^2) H'[t]-13268480 ((G[t])^2) ((H'[t])^3)-4243456 G[t] H[t] ((H'[t])^3)+577536 G'[t] ((H'[t])^3)-512 ((G[t])^6) (1149360 ((H[t])^2)-367304 G'[t]+196647 H'[t])+2625536 ((G[t])^2) ((G''[t])^2)+293888 G[t] H[t] ((G''[t])^2)+5586944 G'[t] ((G''[t])^2)+512 ((G[t])^5) (1506060 ((H[t])^3)+H[t] (-467971 G'[t]+97420 H'[t])+937 (112 G''[t]-65 H''[t]))-3072 ((H[t])^3) G'[t] (8930 G''[t]-3813 H''[t])-1536 G[t] ((H[t])^4) (7256 G''[t]-3203 H''[t])-4096 H[t] G'[t] H'[t] (7025 G''[t]-3151 H''[t])-10240 ((G[t])^2) ((H[t])^3) (4590 G''[t]-1079 H''[t])-3281920 ((G[t])^2) G''[t] H''[t]-335872 G[t] H[t] G''[t] H''[t]-6983680 G'[t] G''[t] H''[t]+656384 ((G[t])^2) ((H''[t])^2)+41984 G[t] H[t] ((H''[t])^2)+1396736 G'[t] ((H''[t])^2)+1024 G[t] (((G'[t])^2) (48448 G''[t]-28575 H''[t])+((H'[t])^2) (18768 G''[t]-4351 H''[t])+6 G'[t] H'[t] (-10748 G''[t]+5033 H''[t]))+512 G[t] ((H[t])^2) (3 G'[t] (15788 G''[t]-8699 H''[t])+H'[t] (-38016 G''[t]+10309 H''[t]))-1024 ((G[t])^2) H[t] (G'[t] (47768 G''[t]-26178 H''[t])+H'[t] (-31325 G''[t]+11971 H''[t]))-1969152 ((G[t])^2) H'[t] Derivative[3][G][t]+1024 (8802 ((H[t])^5) G''[t]+18243 ((H[t])^3) H'[t] G''[t]+10476 H[t] ((H'[t])^2) G''[t]+1956 ((H[t])^4) Derivative[3][G][t]-723 ((H[t])^2) (3 ((G''[t])^2)-3 G''[t] H''[t]-2 H'[t] Derivative[3][G][t])+1364 H'[t] (-3 ((G''[t])^2)+3 G''[t] H''[t]+H'[t] Derivative[3][G][t]))-512 ((G[t])^3) (76218 ((H[t])^5)+((H[t])^3) (-1468770 G'[t]+968346 H'[t])+3 H'[t] (30376 G''[t]-14547 H''[t])-156 ((H[t])^2) (1642 G''[t]-677 H''[t])+G'[t] (-131760 G''[t]+79145 H''[t])+H[t] (687106 ((G'[t])^2)-725450 G'[t] H'[t]+144396 ((H'[t])^2)+3107 (7 Derivative[3][G][t]-3 Derivative[3][H][t])))+512 G[t] H[t] G'[t] (70791 ((H'[t])^2)+82 (7 Derivative[3][G][t]-3 Derivative[3][H][t]))+2048 ((G[t])^2) G'[t] (51782 ((H'[t])^2)+641 (2 Derivative[3][G][t]-Derivative[3][H][t]))+1024 ((G[t])^2) ((H[t])^2) (248850 ((G'[t])^2)-228500 G'[t] H'[t]+31054 ((H'[t])^2)+4381 (3 Derivative[3][G][t]-Derivative[3][H][t]))-1536 G[t] ((H[t])^3) (70590 ((G'[t])^2)-42970 G'[t] H'[t]-304 ((H'[t])^2)+1063 (5 Derivative[3][G][t]-Derivative[3][H][t]))-1396736 G'[t] H'[t] (3 Derivative[3][G][t]-Derivative[3][H][t])-41984 G[t] H[t] H'[t] (5 Derivative[3][G][t]-Derivative[3][H][t])+656384 ((G[t])^2) H'[t] Derivative[3][H][t]-1024 ((G[t])^4) (373157 ((H[t])^4)-259588 ((G'[t])^2)+4 ((H[t])^2) (68487 G'[t]-77527 H'[t])+320295 G'[t] H'[t]-85018 ((H'[t])^2)+2 H[t] (66283 G''[t]-33832 H''[t])-3748 Derivative[3][G][t]+1874 Derivative[3][H][t])+1024 ((H[t])^2) G'[t] (28967 ((H'[t])^2)+723 (-3 Derivative[3][G][t]+Derivative[3][H][t]))-1024 ((G'[t])^2) (14670 ((H[t])^4)+37377 ((H[t])^2) H'[t]-8538 ((H'[t])^2)+H[t] (-14896 G''[t]+9876 H''[t])+1364 (-2 Derivative[3][G][t]+Derivative[3][H][t]))))+α'[t] (((6750 G[t]+3375 H[t])/1125)+(1/1125)Γ (47014912 ((G[t])^7)-102018560 ((G[t])^6) H[t]-78895104 G[t] ((H[t])^6)-6018048 ((H[t])^7)+47106048 G[t] ((G'[t])^3)+6668288 H[t] ((G'[t])^3)+3072 ((H[t])^5) (16853 G'[t]-24408 H'[t])-120367104 G[t] ((G'[t])^2) H'[t]-40955904 H[t] ((G'[t])^2) H'[t]-26155008 G[t] ((H'[t])^3)-27619328 H[t] ((H'[t])^3)+2048 G[t] ((H[t])^4) (5987 G'[t]+31803 H'[t])-4096 ((G[t])^5) (17958 ((H[t])^2)-42287 G'[t]+35827 H'[t])+1396736 G[t] ((G''[t])^2)-1396736 H[t] ((G''[t])^2)+1024 ((G[t])^4) (448808 ((H[t])^3)+H[t] (-416709 G'[t]+331604 H'[t])+22092 G''[t]-21451 H''[t])-2048 G[t] ((H[t])^3) (19677 G''[t]-20441 H''[t])+3072 ((H[t])^4) (6010 G''[t]-6251 H''[t])+12570624 (((G'[t]-H'[t]))^2) (G''[t]-H''[t])-2793472 G[t] G''[t] H''[t]+2793472 H[t] G''[t] H''[t]+1396736 G[t] ((H''[t])^2)-1396736 H[t] ((H''[t])^2)-8192 G[t] H[t] (G'[t] (1500 G''[t]-1159 H''[t])+H'[t] (-818 G''[t]+477 H''[t]))-4096 ((H[t])^2) (G'[t] (4979 G''[t]-5320 H''[t])+H'[t] (-5661 G''[t]+6002 H''[t]))-1396736 G[t] H'[t] Derivative[3][G][t]+512 ((G[t])^2) (723273 ((H[t])^5)+((H[t])^3) (-508076 G'[t]+274896 H'[t])+12 ((H[t])^2) (7785 G''[t]-7826 H''[t])+8 G'[t] (7979 G''[t]-7638 H''[t])+8 H'[t] (-7297 G''[t]+6956 H''[t])+H[t] (-188241 ((G'[t])^2)+282434 G'[t] H'[t]-102377 ((H'[t])^2)-1118 (Derivative[3][G][t]-Derivative[3][H][t])))-512 ((H[t])^3) (101673 ((G'[t])^2)-257474 G'[t] H'[t]+158529 ((H'[t])^2)-1446 (Derivative[3][G][t]-Derivative[3][H][t]))+22528 G[t] G'[t] (4413 ((H'[t])^2)+62 Derivative[3][G][t]-62 Derivative[3][H][t])+1396736 H[t] H'[t] (Derivative[3][G][t]-Derivative[3][H][t])+1396736 G[t] H'[t] Derivative[3][H][t]-1024 ((G[t])^3) (601975 ((H[t])^4)-131103 ((G'[t])^2)+225162 G'[t] H'[t]-95423 ((H'[t])^2)+((H[t])^2) (-439066 G'[t]+316126 H'[t])+6 H[t] (7913 G''[t]-7713 H''[t])-641 Derivative[3][G][t]+641 Derivative[3][H][t])+1024 G[t] ((H[t])^2) (13854 ((G'[t])^2)-44792 G'[t] H'[t]+35030 ((H'[t])^2)-805 Derivative[3][G][t]+805 Derivative[3][H][t])+45056 H[t] G'[t] (1374 ((H'[t])^2)+31 (-Derivative[3][G][t]+Derivative[3][H][t]))))+Ψ''[t] (-3 H[t]+(1/1125)Γ (33561088 ((G[t])^6) H[t]+75331584 G[t] ((H[t])^6)+6018048 ((H[t])^7)+6406144 H[t] ((G'[t])^3)+1024 ((G[t])^4) H[t] (106765 G'[t]-186514 H'[t])-1536 ((H[t])^5) (173641 ((G[t])^2)+21970 G'[t]-48816 H'[t])+6426624 H[t] ((G'[t])^2) H'[t]+27619328 H[t] ((H'[t])^3)+1396736 H[t] ((G''[t])^2)+1024 ((G[t])^3) H[t] (15188 G''[t]-33189 H''[t])-2793472 H[t] G''[t] H''[t]+1396736 H[t] ((H''[t])^2)+1024 ((H[t])^4) (322782 ((G[t])^3)-G[t] (42970 G'[t]+30651 H'[t])-12162 G''[t]+18753 H''[t])+4096 G[t] H[t] (G'[t] (5374 G''[t]-4910 H''[t])+H'[t] (-4569 G''[t]+4105 H''[t]))+3072 (12181 ((G[t])^5) H'[t]+((G[t])^3) (15829 G'[t]-14547 H'[t]) H'[t]+2 G[t] H'[t] (5715 ((G'[t])^2)-10066 G'[t] H'[t]+4351 ((H'[t])^2))+1874 ((G[t])^4) H''[t]+1364 (G'[t]-H'[t]) (H'[t] (2 G''[t]-3 H''[t])+G'[t] H''[t])+1282 ((G[t])^2) (H'[t] (G''[t]-2 H''[t])+G'[t] H''[t]))-1396736 H[t] H'[t] Derivative[3][G][t]-4096 H[t] G'[t] (9876 ((H'[t])^2)-341 (Derivative[3][G][t]-Derivative[3][H][t]))+512 ((G[t])^2) H[t] (132111 ((G'[t])^2)-285662 G'[t] H'[t]+149571 ((H'[t])^2)+1282 (Derivative[3][G][t]-Derivative[3][H][t]))-512 ((H[t])^3) (310108 ((G[t])^4)-37377 ((G'[t])^2)-4 ((G[t])^2) (57125 G'[t]-47239 H'[t])+184502 G'[t] H'[t]-158529 ((H'[t])^2)+G[t] (-19008 G''[t]+58886 H''[t])+1446 (Derivative[3][G][t]-Derivative[3][H][t]))+1396736 H[t] H'[t] Derivative[3][H][t]-1024 ((H[t])^2) (19484 ((G[t])^5)+2 ((G[t])^3) (72545 G'[t]-100938 H'[t])+((G[t])^2) (12530 G''[t]-38257 H''[t])+2 H'[t] (9153 G''[t]-12004 H''[t])+2 G'[t] (-5620 G''[t]+8471 H''[t])+G[t] (-19602 ((G'[t])^2)+21097 G'[t] H'[t]+6063 ((H'[t])^2)+82 (-Derivative[3][G][t]+Derivative[3][H][t])))))+(1/1125)1024 Γ (G[t]-H[t]) (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[3][α][t]+(1/((a[t])^2))(k^2) ((1/10125)Γ α'[t] (43344896 ((G[t])^5)-155692032 ((G[t])^4) H[t]+250450944 ((G[t])^3) ((H[t])^2)-219223040 ((G[t])^2) ((H[t])^3)+93136896 G[t] ((H[t])^4)-12017664 ((H[t])^5)+40883200 ((G[t])^3) G'[t]-18108416 ((G[t])^2) H[t] G'[t]-15199232 G[t] ((H[t])^2) G'[t]-7575552 ((H[t])^3) G'[t]+39471104 G[t] ((G'[t])^2)+335872 H[t] ((G'[t])^2)-36944896 ((G[t])^3) H'[t]+14673920 ((G[t])^2) H[t] H'[t]+10253312 G[t] ((H[t])^2) H'[t]+12017664 ((H[t])^3) H'[t]-70561792 G[t] G'[t] H'[t]-9052160 H[t] G'[t] H'[t]+31090688 G[t] ((H'[t])^2)+8716288 H[t] ((H'[t])^2)+3938304 ((G[t])^2) G''[t]-4442112 ((H[t])^2) G''[t]+8380416 G'[t] G''[t]-8380416 H'[t] G''[t]+503808 G[t] H[t] (G''[t]-H''[t])-3938304 ((G[t])^2) H''[t]+4442112 ((H[t])^2) H''[t]-8380416 G'[t] H''[t]+8380416 H'[t] H''[t])+(1/10125)Γ (OverBar[Ψ])'[t] (-41474048 ((G[t])^6)+214175744 ((G[t])^5) H[t]-410521600 ((G[t])^4) ((H[t])^2)+326385664 ((G[t])^3) ((H[t])^3)-70539264 ((G[t])^2) ((H[t])^4)-18026496 G[t] ((H[t])^5)+18655232 ((G[t])^4) G'[t]-4464640 ((G[t])^3) H[t] G'[t]-161536000 ((G[t])^2) ((H[t])^2) G'[t]+183398400 G[t] ((H[t])^3) G'[t]-36052992 ((H[t])^4) G'[t]+466944 ((G[t])^2) ((G'[t])^2)-76967936 G[t] H[t] ((G'[t])^2)+32919552 ((H[t])^2) ((G'[t])^2)-8716288 ((G'[t])^3)-22761472 ((G[t])^4) H'[t]+35403776 ((G[t])^3) H[t] H'[t]+75923456 ((G[t])^2) ((H[t])^2) H'[t]-88565760 G[t] ((H[t])^3) H'[t]+5836800 ((G[t])^2) G'[t] H'[t]+114245632 G[t] H[t] G'[t] H'[t]-32919552 ((H[t])^2) G'[t] H'[t]+17432576 ((G'[t])^2) H'[t]-6303744 ((G[t])^2) ((H'[t])^2)-37277696 G[t] H[t] ((H'[t])^2)-8716288 G'[t] ((H'[t])^2)+7743488 ((G[t])^3) G''[t]-24203264 ((G[t])^2) H[t] G''[t]+16459776 G[t] ((H[t])^2) G''[t]-8716288 G[t] G'[t] G''[t]+8716288 G[t] H'[t] G''[t]-7743488 ((G[t])^3) H''[t]+24203264 ((G[t])^2) H[t] H''[t]-16459776 G[t] ((H[t])^2) H''[t]+8716288 G[t] G'[t] H''[t]-8716288 G[t] H'[t] H''[t])+(1/10125)Γ Ψ'[t] (-1870848 ((G[t])^5) H[t]-58483712 ((G[t])^4) ((H[t])^2)+160070656 ((G[t])^3) ((H[t])^3)-107162624 ((G[t])^2) ((H[t])^4)-22597632 G[t] ((H[t])^5)+30044160 ((H[t])^6)-71388160 ((G[t])^3) H[t] G'[t]+85458944 ((G[t])^2) ((H[t])^2) G'[t]+50459648 G[t] ((H[t])^3) G'[t]-64530432 ((H[t])^4) G'[t]-24451072 G[t] H[t] ((G'[t])^2)+28225536 ((H[t])^2) ((G'[t])^2)+6092800 ((G[t])^4) H'[t]+15909888 ((G[t])^3) H[t] H'[t]+49281024 ((G[t])^2) ((H[t])^2) H'[t]-177875968 G[t] ((H[t])^3) H'[t]+106592256 ((H[t])^4) H'[t]-19425280 ((G[t])^2) G'[t] H'[t]+97140736 G[t] H[t] G'[t] H'[t]-85264384 ((H[t])^2) G'[t] H'[t]+4526080 ((G'[t])^2) H'[t]+19425280 ((G[t])^2) ((H'[t])^2)-72689664 G[t] H[t] ((H'[t])^2)+57038848 ((H[t])^2) ((H'[t])^2)-9052160 G'[t] ((H'[t])^2)+4526080 ((H'[t])^3)-11681792 ((G[t])^2) H[t] G''[t]+23699456 G[t] ((H[t])^2) G''[t]-12017664 ((H[t])^3) G''[t]+335872 H[t] G'[t] G''[t]-335872 H[t] H'[t] G''[t]+11681792 ((G[t])^2) H[t] H''[t]-23699456 G[t] ((H[t])^2) H''[t]+12017664 ((H[t])^3) H''[t]-335872 H[t] G'[t] H''[t]+335872 H[t] H'[t] H''[t])+(1/10125)Γ (2878464 ((G[t])^4)-9544704 ((G[t])^3) H[t]+13458432 ((G[t])^2) ((H[t])^2)-9796608 G[t] ((H[t])^3)+3004416 ((H[t])^4)+1969152 ((G[t])^2) G'[t]+251904 G[t] H[t] G'[t]-2221056 ((H[t])^2) G'[t]+2095104 ((G'[t])^2)-1969152 ((G[t])^2) H'[t]-251904 G[t] H[t] H'[t]+2221056 ((H[t])^2) H'[t]-4190208 G'[t] H'[t]+2095104 ((H'[t])^2)) α''[t]+(1/10125)Γ (-37420032 ((G[t])^5)+121202688 ((G[t])^4) H[t]-165414912 ((G[t])^3) ((H[t])^2)+113897472 ((G[t])^2) ((H[t])^3)-29260800 G[t] ((H[t])^4)-3004416 ((H[t])^5)-48626688 ((G[t])^3) G'[t]+52024320 ((G[t])^2) H[t] G'[t]-25211904 G[t] ((H[t])^2) G'[t]+21814272 ((H[t])^3) G'[t]-35112960 G[t] ((G'[t])^2)-2598912 H[t] ((G'[t])^2)+44688384 ((G[t])^3) H'[t]-48589824 ((G[t])^2) H[t] H'[t]+30157824 G[t] ((H[t])^2) H'[t]-26256384 ((H[t])^3) H'[t]+61845504 G[t] G'[t] H'[t]+13578240 H[t] G'[t] H'[t]-26732544 G[t] ((H'[t])^2)-10979328 H[t] ((H'[t])^2)-3938304 ((G[t])^2) G''[t]-503808 G[t] H[t] G''[t]+4442112 ((H[t])^2) G''[t]-8380416 G'[t] G''[t]+8380416 H'[t] G''[t]+3938304 ((G[t])^2) H''[t]+503808 G[t] H[t] H''[t]-4442112 ((H[t])^2) H''[t]+8380416 G'[t] H''[t]-8380416 H'[t] H''[t]) χ''[t]+(1/10125)Γ (3046400 ((G[t])^4) H[t]-21898240 ((G[t])^3) ((H[t])^2)+49679360 ((G[t])^2) ((H[t])^3)-45849600 G[t] ((H[t])^4)+15022080 ((H[t])^5)-9712640 ((G[t])^2) H[t] G'[t]+23951360 G[t] ((H[t])^2) G'[t]-14238720 ((H[t])^3) G'[t]+2263040 H[t] ((G'[t])^2)+9712640 ((G[t])^2) H[t] H'[t]-23951360 G[t] ((H[t])^2) H'[t]+14238720 ((H[t])^3) H'[t]-4526080 H[t] G'[t] H'[t]+2263040 H[t] ((H'[t])^2)) Ψ''[t]+(1/10125)Γ (-5924864 ((G[t])^5)+31442944 ((G[t])^4) H[t]-63137792 ((G[t])^3) ((H[t])^2)+55646208 ((G[t])^2) ((H[t])^3)-18026496 G[t] ((H[t])^4)+7743488 ((G[t])^3) G'[t]-24203264 ((G[t])^2) H[t] G'[t]+16459776 G[t] ((H[t])^2) G'[t]-4358144 G[t] ((G'[t])^2)-7743488 ((G[t])^3) H'[t]+24203264 ((G[t])^2) H[t] H'[t]-16459776 G[t] ((H[t])^2) H'[t]+8716288 G[t] G'[t] H'[t]-4358144 G[t] ((H'[t])^2)) (OverBar[Ψ])''[t]+χ'[t] (1+(1/10125)Γ (-100683264 ((G[t])^6)+209534976 ((G[t])^5) H[t]+26056704 ((G[t])^4) ((H[t])^2)-444463104 ((G[t])^3) ((H[t])^3)+506049024 ((G[t])^2) ((H[t])^4)-226510848 G[t] ((H[t])^5)+30016512 ((H[t])^6)-327982080 ((G[t])^4) G'[t]+640223232 ((G[t])^3) H[t] G'[t]-535443456 ((G[t])^2) ((H[t])^2) G'[t]+235874304 G[t] ((H[t])^3) G'[t]-12672000 ((H[t])^4) G'[t]-202922496 ((G[t])^2) ((G'[t])^2)+80234496 G[t] H[t] ((G'[t])^2)-21874176 ((H[t])^2) ((G'[t])^2)-19218432 ((G'[t])^3)+278446080 ((G[t])^4) H'[t]-531744768 ((G[t])^3) H[t] H'[t]+442275840 ((G[t])^2) ((H[t])^2) H'[t]-176830464 G[t] ((H[t])^3) H'[t]-12146688 ((H[t])^4) H'[t]+329963520 ((G[t])^2) G'[t] H'[t]-100890624 G[t] H[t] G'[t] H'[t]+60051456 ((H[t])^2) G'[t] H'[t]+38799360 ((G'[t])^2) H'[t]-131231232 ((G[t])^2) ((H'[t])^2)+29036544 G[t] H[t] ((H'[t])^2)-42367488 ((H[t])^2) ((H'[t])^2)-19943424 G'[t] ((H'[t])^2)+362496 ((H'[t])^3)-46657536 ((G[t])^3) G''[t]+54245376 ((G[t])^2) H[t] G''[t]-27181056 G[t] ((H[t])^2) G''[t]+19593216 ((H[t])^3) G''[t]-66035712 G[t] G'[t] G''[t]-1007616 H[t] G'[t] G''[t]+57655296 G[t] H'[t] G''[t]+9388032 H[t] H'[t] G''[t]-4190208 ((G''[t])^2)+44688384 ((G[t])^3) H''[t]-52528128 ((G[t])^2) H[t] H''[t]+29654016 G[t] ((H[t])^2) H''[t]-21814272 ((H[t])^3) H''[t]+61845504 G[t] G'[t] H''[t]+5197824 H[t] G'[t] H''[t]-53465088 G[t] H'[t] H''[t]-13578240 H[t] H'[t] H''[t]+8380416 G''[t] H''[t]-4190208 ((H''[t])^2)-1969152 ((G[t])^2) Derivative[3][G][t]-251904 G[t] H[t] Derivative[3][G][t]+2221056 ((H[t])^2) Derivative[3][G][t]-4190208 G'[t] Derivative[3][G][t]+4190208 H'[t] Derivative[3][G][t]+1969152 ((G[t])^2) Derivative[3][H][t]+251904 G[t] H[t] Derivative[3][H][t]-2221056 ((H[t])^2) Derivative[3][H][t]+4190208 G'[t] Derivative[3][H][t]-4190208 H'[t] Derivative[3][H][t]))+(OverBar[Ψ])[t] (-6 G[t]+(1/10125)Γ (-141422592 ((G[t])^7)+975872000 ((G[t])^6) H[t]-1941645312 ((G[t])^5) ((H[t])^2)+1245659136 ((G[t])^4) ((H[t])^3)+268460032 ((G[t])^3) ((H[t])^4)-538140672 ((G[t])^2) ((H[t])^5)+131217408 G[t] ((H[t])^6)+205372416 ((G[t])^5) G'[t]+469512192 ((G[t])^4) H[t] G'[t]-1991995392 ((G[t])^3) ((H[t])^2) G'[t]+1718052864 ((G[t])^2) ((H[t])^3) G'[t]-18026496 ((H[t])^5) G'[t]+301541376 ((G[t])^3) ((G'[t])^2)-456314880 ((G[t])^2) H[t] ((G'[t])^2)+72105984 ((H[t])^3) ((G'[t])^2)-13188096 G[t] ((G'[t])^3)-28561408 H[t] ((G'[t])^3)-9216 G[t] ((H[t])^4) (41549 G'[t]-26322 H'[t])-132824064 ((G[t])^5) H'[t]-532271104 ((G[t])^4) H[t] H'[t]+1723483136 ((G[t])^3) ((H[t])^2) H'[t]-1300971520 ((G[t])^2) ((H[t])^3) H'[t]-471581696 ((G[t])^3) G'[t] H'[t]+620277760 ((G[t])^2) H[t] G'[t] H'[t]-88565760 ((H[t])^3) G'[t] H'[t]+14442496 G[t] ((G'[t])^2) H'[t]+65839104 H[t] ((G'[t])^2) H'[t]+177531904 ((G[t])^3) ((H'[t])^2)-195405824 ((G[t])^2) H[t] ((H'[t])^2)+1963008 G[t] G'[t] ((H'[t])^2)-37277696 H[t] G'[t] ((H'[t])^2)-3217408 G[t] ((H'[t])^3)+116355072 ((G[t])^4) G''[t]-194420736 ((G[t])^3) H[t] G''[t]+17719296 ((G[t])^2) ((H[t])^2) G''[t]+78372864 G[t] ((H[t])^3) G''[t]-18026496 ((H[t])^4) G''[t]+41926656 ((G[t])^2) G'[t] G''[t]-79380480 G[t] H[t] G'[t] G''[t]+32919552 ((H[t])^2) G'[t] G''[t]-13074432 ((G'[t])^2) G''[t]-34686976 ((G[t])^2) H'[t] G''[t]-16459776 ((H[t])^2) H'[t] G''[t]+17432576 G'[t] H'[t] G''[t]-4358144 ((H'[t])^2) G''[t]-251904 G[t] ((G''[t])^2)+2048 G[t] H[t] H'[t] (27188 G''[t]-15493 H''[t])-112735232 ((G[t])^4) H''[t]+196977664 ((G[t])^3) H[t] H''[t]-51719168 ((G[t])^2) ((H[t])^2) H''[t]-32523264 G[t] ((H[t])^3) H''[t]-34435072 ((G[t])^2) G'[t] H''[t]+55429120 G[t] H[t] G'[t] H''[t]-16459776 ((H[t])^2) G'[t] H''[t]+8716288 ((G'[t])^2) H''[t]+27195392 ((G[t])^2) H'[t] H''[t]-8716288 G'[t] H'[t] H''[t]+503808 G[t] G''[t] H''[t]-251904 G[t] ((H''[t])^2)+9544704 ((G[t])^3) Derivative[3][G][t]-19341312 ((G[t])^2) H[t] Derivative[3][G][t]-251904 G[t] G'[t] Derivative[3][G][t]+251904 G[t] H'[t] Derivative[3][G][t]+1024 G[t] ((H[t])^2) (69906 ((G'[t])^2)-37073 G'[t] H'[t]+6631 ((H'[t])^2)+9567 (Derivative[3][G][t]-Derivative[3][H][t]))-9544704 ((G[t])^3) Derivative[3][H][t]+19341312 ((G[t])^2) H[t] Derivative[3][H][t]+251904 G[t] G'[t] Derivative[3][H][t]-251904 G[t] H'[t] Derivative[3][H][t]))+Ψ[t] (-2 H[t]+(1/10125)Γ (-293888 ((G[t])^6) H[t]-564934656 ((G[t])^5) ((H[t])^2)+1560913920 ((G[t])^4) ((H[t])^3)-1352452096 ((G[t])^3) ((H[t])^4)+235355136 ((G[t])^2) ((H[t])^5)+169426944 G[t] ((H[t])^6)-48015360 ((H[t])^7)-564430848 ((G[t])^4) H[t] G'[t]+161851392 ((H[t])^5) G'[t]-52878336 ((H[t])^3) ((G'[t])^2)-29892608 H[t] ((G'[t])^3)+2048 ((G[t])^2) ((H[t])^3) (407289 G'[t]-550459 H'[t])-3072 G[t] ((H[t])^4) (261148 G'[t]-232882 H'[t])-1870848 ((G[t])^5) H'[t]+344375296 ((G[t])^4) H[t] H'[t]-80824320 ((H[t])^5) H'[t]-71388160 ((G[t])^3) G'[t] H'[t]-38166528 ((H[t])^3) G'[t] H'[t]-24451072 G[t] ((G'[t])^2) H'[t]+96242688 H[t] ((G'[t])^2) H'[t]+59706368 ((G[t])^3) ((H'[t])^2)+99124224 ((H[t])^3) ((H'[t])^2)+49238016 G[t] G'[t] ((H'[t])^2)-103143424 H[t] G'[t] ((H'[t])^2)-24786944 G[t] ((H'[t])^3)+36793344 H[t] ((H'[t])^3)+5120 ((G[t])^3) ((H[t])^2) (72402 G'[t]+29345 H'[t])-161193984 ((G[t])^3) H[t] G''[t]+244224000 ((G[t])^2) ((H[t])^2) G''[t]-67878912 G[t] ((H[t])^3) G''[t]-15151104 ((H[t])^4) G''[t]+30302208 ((H[t])^2) G'[t] G''[t]-11681792 ((G[t])^2) H'[t] G''[t]-34443264 ((H[t])^2) H'[t] G''[t]+335872 G'[t] H'[t] G''[t]-335872 ((H'[t])^2) G''[t]-3938304 H[t] ((G''[t])^2)+2048 G[t] H[t] H'[t] (57136 G''[t]-66908 H''[t])+3046400 ((G[t])^4) H''[t]+127781888 ((G[t])^3) H[t] H''[t]-163941376 ((G[t])^2) ((H[t])^2) H''[t]-4635648 G[t] ((H[t])^3) H''[t]+37748736 ((H[t])^4) H''[t]-9712640 ((G[t])^2) G'[t] H''[t]-40602624 ((H[t])^2) G'[t] H''[t]+2263040 ((G'[t])^2) H''[t]+21394432 ((G[t])^2) H'[t] H''[t]+44743680 ((H[t])^2) H'[t] H''[t]-4861952 G'[t] H'[t] H''[t]+2598912 ((H'[t])^2) H''[t]+7876608 H[t] G''[t] H''[t]-3938304 H[t] ((H''[t])^2)+2048 G[t] H[t] G'[t] (-49410 G''[t]+59182 H''[t])-7575552 ((H[t])^3) Derivative[3][G][t]-3938304 H[t] G'[t] Derivative[3][G][t]+3938304 H[t] H'[t] Derivative[3][G][t]+1024 ((G[t])^2) H[t] (-448413 ((G'[t])^2)+802754 G'[t] H'[t]-323635 ((H'[t])^2)-11244 (Derivative[3][G][t]-Derivative[3][H][t]))+1024 G[t] ((H[t])^2) (330828 ((G'[t])^2)-357319 G'[t] H'[t]-697 ((H'[t])^2)+18642 (Derivative[3][G][t]-Derivative[3][H][t]))+7575552 ((H[t])^3) Derivative[3][H][t]+3938304 H[t] G'[t] Derivative[3][H][t]-3938304 H[t] H'[t] Derivative[3][H][t]))+α[t] (-1+(1/10125)Γ (142157312 ((G[t])^6)-421839872 ((G[t])^5) H[t]-60060672 ((H[t])^6)+27934720 ((G'[t])^3)+1024 ((G[t])^4) (432567 ((H[t])^2)+302077 G'[t]-255642 H'[t])+9216 ((H[t])^4) (12289 G'[t]-10248 H'[t])-60758016 ((G'[t])^2) H'[t]+37711872 G'[t] ((H'[t])^2)-4888576 ((H'[t])^3)+4190208 ((G''[t])^2)-9216 ((H[t])^3) (822 G''[t]-1063 H''[t])-8380416 G''[t] H''[t]+4190208 ((H''[t])^2)-1024 ((G[t])^3) (41009 ((H[t])^3)+H[t] (551143 G'[t]-469171 H'[t])-38002 G''[t]+36079 H''[t])+4096 H[t] (G'[t] (164 G''[t]-1187 H''[t])+H'[t] (-2210 G''[t]+3233 H''[t]))+4190208 G'[t] Derivative[3][G][t]-4190208 H'[t] Derivative[3][G][t]+1024 G[t] (260874 ((H[t])^5)+((H[t])^3) (-458723 G'[t]+432883 H'[t])+G'[t] (73000 G''[t]-68908 H''[t])+((H[t])^2) (-12674 G''[t]+10259 H''[t])+4 H'[t] (-16204 G''[t]+15181 H''[t])+2 H[t] (10344 ((G'[t])^2)-53953 G'[t] H'[t]+39517 ((H'[t])^2)+123 (Derivative[3][G][t]-Derivative[3][H][t])))-512 ((H[t])^2) (76701 ((G'[t])^2)-113540 G'[t] H'[t]+28655 ((H'[t])^2)+4338 (Derivative[3][G][t]-Derivative[3][H][t]))-4190208 G'[t] Derivative[3][H][t]+4190208 H'[t] Derivative[3][H][t]-512 ((G[t])^2) (641303 ((H[t])^4)-395421 ((G'[t])^2)-8 ((H[t])^2) (149297 G'[t]-138545 H'[t])+617920 G'[t] H'[t]-230683 ((H'[t])^2)+H[t] (35860 G''[t]-32506 H''[t])-3846 Derivative[3][G][t]+3846 Derivative[3][H][t])))+χ[t] (((60750 G[t]+20250 H[t])/10125)+(1/10125)Γ (141422592 ((G[t])^7)-975578112 ((G[t])^6) H[t]+2506579968 ((G[t])^5) ((H[t])^2)-2806573056 ((G[t])^4) ((H[t])^3)+1083992064 ((G[t])^3) ((H[t])^4)+302785536 ((G[t])^2) ((H[t])^5)-300644352 G[t] ((H[t])^6)+48015360 ((H[t])^7)-143824896 ((H[t])^5) G'[t]-19227648 ((H[t])^3) ((G'[t])^2)+13188096 G[t] ((G'[t])^3)+58454016 H[t] ((G'[t])^3)-6144 ((G[t])^2) ((H[t])^3) (415394 G'[t]-395233 H'[t])+3072 G[t] ((H[t])^4) (385795 G'[t]-311848 H'[t])+6144 ((G[t])^3) ((H[t])^2) (263883 G'[t]-304969 H'[t])-3072 ((G[t])^5) (66853 G'[t]-43846 H'[t])+80824320 ((H[t])^5) H'[t]+126732288 ((H[t])^3) G'[t] H'[t]+10008576 G[t] ((G'[t])^2) H'[t]-162081792 H[t] ((G'[t])^2) H'[t]-99124224 ((H[t])^3) ((H'[t])^2)+140421120 H[t] G'[t] ((H'[t])^2)+28004352 G[t] ((H'[t])^3)-36793344 H[t] ((H'[t])^3)+6144 ((G[t])^4) H[t] (15449 G'[t]+30582 H'[t])-116355072 ((G[t])^4) G''[t]+355614720 ((G[t])^3) H[t] G''[t]-261943296 ((G[t])^2) ((H[t])^2) G''[t]+33177600 ((H[t])^4) G''[t]-63221760 ((H[t])^2) G'[t] G''[t]+13074432 ((G'[t])^2) G''[t]+46368768 ((G[t])^2) H'[t] G''[t]+50903040 ((H[t])^2) H'[t] G''[t]-17768448 G'[t] H'[t] G''[t]+4694016 ((H'[t])^2) G''[t]+251904 G[t] ((G''[t])^2)+3938304 H[t] ((G''[t])^2)-172032 G[t] ((H[t])^3) (61 G''[t]-216 H''[t])+109688832 ((G[t])^4) H''[t]-324759552 ((G[t])^3) H[t] H''[t]+215660544 ((G[t])^2) ((H[t])^2) H''[t]-37748736 ((H[t])^4) H''[t]+57062400 ((H[t])^2) G'[t] H''[t]-10979328 ((G'[t])^2) H''[t]-48589824 ((G[t])^2) H'[t] H''[t]-44743680 ((H[t])^2) H'[t] H''[t]+13578240 G'[t] H'[t] H''[t]-2598912 ((H'[t])^2) H''[t]-503808 G[t] G''[t] H''[t]-7876608 H[t] G''[t] H''[t]+251904 G[t] ((H''[t])^2)+3938304 H[t] ((H''[t])^2)+1024 ((G[t])^2) G'[t] (-40944 G''[t]+43113 H''[t])+6144 G[t] H[t] (G'[t] (29390 G''[t]-28749 H''[t])+H'[t] (-28108 G''[t]+27467 H''[t]))+7575552 ((H[t])^3) Derivative[3][G][t]+3938304 H[t] G'[t] Derivative[3][G][t]-251904 G[t] H'[t] Derivative[3][G][t]-3938304 H[t] H'[t] Derivative[3][G][t]-3072 ((G[t])^3) (98158 ((G'[t])^2)-176748 G'[t] H'[t]+77226 ((H'[t])^2)+3107 (Derivative[3][G][t]-Derivative[3][H][t]))-3072 G[t] ((H[t])^2) (133578 ((G'[t])^2)-131464 G'[t] H'[t]+1978 ((H'[t])^2)+9403 (Derivative[3][G][t]-Derivative[3][H][t]))+3072 ((G[t])^2) H[t] (298011 ((G'[t])^2)-469498 G'[t] H'[t]+171487 ((H'[t])^2)+10044 (Derivative[3][G][t]-Derivative[3][H][t]))-7575552 ((H[t])^3) Derivative[3][H][t]-3938304 H[t] G'[t] Derivative[3][H][t]+251904 G[t] H'[t] Derivative[3][H][t]+3938304 H[t] H'[t] Derivative[3][H][t]-3072 G[t] G'[t] (16667 ((H'[t])^2)+82 (-Derivative[3][G][t]+Derivative[3][H][t]))))+(1/10125)Γ (-2878464 ((G[t])^4)+9544704 ((G[t])^3) H[t]-13458432 ((G[t])^2) ((H[t])^2)+9796608 G[t] ((H[t])^3)-3004416 ((H[t])^4)-1969152 ((G[t])^2) G'[t]-251904 G[t] H[t] G'[t]+2221056 ((H[t])^2) G'[t]-2095104 ((G'[t])^2)+1969152 ((G[t])^2) H'[t]+251904 G[t] H[t] H'[t]-2221056 ((H[t])^2) H'[t]+4190208 G'[t] H'[t]-2095104 ((H'[t])^2)) Derivative[3][χ][t])+(1/1125)1024 Γ (12181 ((G[t])^5) H[t]+6846 ((H[t])^6)+((G[t])^3) H[t] (35204 ((H[t])^2)+15829 G'[t]-26975 H'[t])-3 ((H[t])^4) (3813 G'[t]-5599 H'[t])-4 ((G[t])^4) (8458 ((H[t])^2)-937 H'[t])+2728 (((G'[t]-H'[t]))^2) H'[t]+2 ((H[t])^2) (2469 ((G'[t])^2)-7748 G'[t] H'[t]+5279 ((H'[t])^2))+G[t] H[t] (-9609 ((H[t])^4)+((H[t])^2) (8699 G'[t]-23065 H'[t])+2 (5715 ((G'[t])^2)-9902 G'[t] H'[t]+4187 ((H'[t])^2))+164 H[t] (G''[t]-H''[t]))+((G[t])^2) (-10790 ((H[t])^4)+2564 (G'[t]-H'[t]) H'[t]+((H[t])^2) (-13089 G'[t]+29495 H'[t])+1282 H[t] (G''[t]-H''[t]))-1446 ((H[t])^3) (G''[t]-H''[t])+2728 H[t] (G'[t]-H'[t]) (G''[t]-H''[t])) Derivative[3][Ψ][t]-(1/1125)2048 Γ (6559 ((G[t])^6)-18938 ((G[t])^5) H[t]+2 G'[t] (978 ((H[t])^4)-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2))+((G[t])^4) (21346 ((H[t])^2)+10109 G'[t]-7594 H'[t])+((G[t])^3) (-9180 ((H[t])^3)+H[t] (-13038 G'[t]+6265 H'[t])+641 (G''[t]-H''[t]))+((G[t])^2) (-2721 ((H[t])^4)+((H[t])^2) (12709 G'[t]-4752 H'[t])+6 (1223 ((G'[t])^2)-2005 G'[t] H'[t]+782 ((H'[t])^2))+82 H[t] (G''[t]-H''[t]))+G[t] (2934 ((H[t])^5)+((H[t])^3) (-11736 G'[t]+6081 H'[t])+12 H[t] (191 ((G'[t])^2)-482 G'[t] H'[t]+291 ((H'[t])^2))-723 ((H[t])^2) (G''[t]-H''[t])+1364 (G'[t]-H'[t]) (G''[t]-H''[t]))) Derivative[3][(OverBar[Ψ])][t]+(OverBar[Ψ])[t] (-((2 (23625 G[t] G'[t]+10125 H[t] G'[t]+3375 G''[t]))/1125)-(1/1125)2 Γ (92378112 G[t] ((H[t])^6) G'[t]-18865152 ((H[t])^7) G'[t]+27884544 G[t] ((G'[t])^4)+2198016 H[t] ((G'[t])^4)+10752 G[t] ((G'[t])^3) (7900 ((H[t])^2)-6291 H'[t])+266712576 G[t] ((H[t])^4) G'[t] H'[t]-10036224 H[t] ((G'[t])^3) H'[t]-13268480 G[t] G'[t] ((H'[t])^3)-4243456 H[t] G'[t] ((H'[t])^3)-1781760 ((H[t])^6) G''[t]+11150336 ((G'[t])^3) G''[t]-20615168 ((G'[t])^2) H'[t] G''[t]+9176064 G'[t] ((H'[t])^2) G''[t]+288768 ((H'[t])^3) G''[t]+13059072 G[t] G'[t] ((G''[t])^2)+4400128 H[t] G'[t] ((G''[t])^2)+698368 ((G''[t])^3)+3584 ((G[t])^6) (46036 H[t] G'[t]+6559 G''[t])-2048 G[t] ((H[t])^3) G'[t] (30357 G''[t]-5395 H''[t])-5852160 ((G'[t])^3) H''[t]+10307584 ((G'[t])^2) H'[t] H''[t]-4455424 G'[t] ((H'[t])^2) H''[t]-13017088 G[t] G'[t] G''[t] H''[t]-5140480 H[t] G'[t] G''[t] H''[t]-1396736 ((G''[t])^2) H''[t]+656384 G[t] G'[t] ((H''[t])^2)+41984 H[t] G'[t] ((H''[t])^2)+698368 G''[t] ((H''[t])^2)-512 ((G[t])^5) (1149360 ((H[t])^2) G'[t]-275478 ((G'[t])^2)+196647 G'[t] H'[t]+66853 H[t] G''[t]-13118 Derivative[3][G][t])+2095104 G'[t] G''[t] Derivative[3][G][t]-2095104 H'[t] G''[t] Derivative[3][G][t]-1396736 G'[t] H''[t] Derivative[3][G][t]+1396736 H'[t] H''[t] Derivative[3][G][t]+1536 ((H[t])^5) (33725 ((G'[t])^2)-24522 G'[t] H'[t]+1956 Derivative[3][G][t])+2048 H[t] H'[t] (-2810 ((G''[t])^2)+3151 G''[t] H''[t]+1746 H'[t] Derivative[3][G][t])-512 G[t] ((G'[t])^2) (558386 ((H[t])^4)+228500 ((H[t])^2) H'[t]+H[t] (14417 G''[t]-26178 H''[t])-2 (51782 ((H'[t])^2)+6697 Derivative[3][G][t]-641 Derivative[3][H][t]))+1024 G[t] ((H[t])^2) G'[t] (31054 ((H'[t])^2)+8328 Derivative[3][G][t]-4381 Derivative[3][H][t])-1024 G[t] G'[t] H'[t] (11389 Derivative[3][G][t]-641 Derivative[3][H][t])+512 H[t] ((G'[t])^2) (23597 ((H'[t])^2)+4338 Derivative[3][G][t]-82 Derivative[3][H][t])-1024 H[t] G'[t] H'[t] (5661 Derivative[3][G][t]-41 Derivative[3][H][t])-698368 G'[t] G''[t] Derivative[3][H][t]+698368 H'[t] G''[t] Derivative[3][H][t]-512 ((H[t])^3) (42354 ((G'[t])^3)-42970 ((G'[t])^2) H'[t]-3 (-3572 ((G''[t])^2)+3813 G''[t] H''[t]+4054 H'[t] Derivative[3][G][t])-3 G'[t] (304 ((H'[t])^2)-4635 Derivative[3][G][t]+1063 Derivative[3][H][t]))-1024 G[t] H[t] G'[t] (H'[t] (7072 G''[t]+11971 H''[t])-41 Derivative[4][G][t])+349184 ((G'[t])^2) Derivative[4][G][t]-698368 G'[t] H'[t] Derivative[4][G][t]+349184 ((H'[t])^2) Derivative[4][G][t]+1536 ((H[t])^4) (10985 H'[t] G''[t]+G'[t] (-6704 G''[t]+3203 H''[t])+326 Derivative[4][G][t])+512 ((G[t])^4) (1506060 ((H[t])^3) G'[t]-91316 ((H[t])^2) G''[t]-106765 H'[t] G''[t]+G'[t] (195384 G''[t]-60905 H''[t])+H[t] (-334265 ((G'[t])^2)+97420 G'[t] H'[t]-37876 Derivative[3][G][t])+937 Derivative[4][G][t])-512 ((G[t])^2) (76218 ((H[t])^5) G'[t]+279193 ((H[t])^4) G''[t]-51782 ((H'[t])^2) G''[t]+((G'[t])^2) (-131103 G''[t]+47487 H''[t])-1923 G''[t] Derivative[3][G][t]+1282 H''[t] Derivative[3][G][t]+((H[t])^3) (-881262 ((G'[t])^2)+968346 G'[t] H'[t]+18360 Derivative[3][G][t])+H[t] (294474 ((G'[t])^3)-435270 ((G'[t])^2) H'[t]+13648 ((G''[t])^2)-13089 G''[t] H''[t]-12530 H'[t] Derivative[3][G][t]+G'[t] (144396 ((H'[t])^2)+22969 Derivative[3][G][t]-9321 Derivative[3][H][t]))+641 G''[t] Derivative[3][H][t]+((H[t])^2) (114250 H'[t] G''[t]-12 G'[t] (24498 G''[t]-8801 H''[t])-4381 Derivative[4][G][t])+G'[t] (3 H'[t] (59225 G''[t]-14547 H''[t])-641 Derivative[4][G][t])+641 H'[t] Derivative[4][G][t])+512 ((H[t])^2) (28967 ((H'[t])^2) G''[t]+((G'[t])^2) (17668 G''[t]-8699 H''[t])+723 (2 H''[t] Derivative[3][G][t]+G''[t] (-3 Derivative[3][G][t]+Derivative[3][H][t]))+G'[t] (H'[t] (-46881 G''[t]+10309 H''[t])-723 Derivative[4][G][t])+723 H'[t] Derivative[4][G][t])-512 ((G[t])^3) (746314 ((H[t])^4) G'[t]-259588 ((G'[t])^3)+427060 ((G'[t])^2) H'[t]-293754 ((H[t])^3) G''[t]-16470 ((G''[t])^2)+15829 G''[t] H''[t]+4 ((H[t])^2) (91316 ((G'[t])^2)-155054 G'[t] H'[t]-10673 Derivative[3][G][t])+15188 H'[t] Derivative[3][G][t]-2 G'[t] (85018 ((H'[t])^2)+10109 Derivative[3][G][t]-1874 Derivative[3][H][t])+H[t] (-145090 H'[t] G''[t]+4 G'[t] (86955 G''[t]-33832 H''[t])+3107 Derivative[4][G][t]))+512 G[t] (101175 ((H[t])^5) G''[t]-5442 ((H[t])^4) Derivative[3][G][t]+((H[t])^2) (7894 ((G''[t])^2)-8699 G''[t] H''[t]-9504 H'[t] Derivative[3][G][t])+4 H'[t] (-5374 ((G''[t])^2)+5033 G''[t] H''[t]+2346 H'[t] Derivative[3][G][t])+((H[t])^3) (42970 H'[t] G''[t]-3189 Derivative[4][G][t])+H[t] (23597 ((H'[t])^2) G''[t]+82 (-2 H''[t] Derivative[3][G][t]+G''[t] (3 Derivative[3][G][t]-Derivative[3][H][t]))-82 H'[t] Derivative[4][G][t]))))+Ψ[t] (((-20250 G[t] H'[t]-13500 H[t] H'[t]-3375 H''[t])/1125)+(1/1125)Γ (-47140864 ((G[t])^7) H'[t]+264112128 G[t] ((H[t])^6) H'[t]-23998464 ((H[t])^7) H'[t]-518016000 G[t] ((H[t])^4) G'[t] H'[t]-4396032 G[t] ((G'[t])^3) H'[t]-6672384 H[t] ((G'[t])^3) H'[t]-59324416 H[t] G'[t] ((H'[t])^3)-1024 G[t] (2736 ((H[t])^2)+23597 G'[t]) ((H'[t])^3)+8486912 G[t] ((H'[t])^4)+27722752 H[t] ((H'[t])^4)-4358144 ((G'[t])^2) H'[t] G''[t]+11509760 G'[t] ((H'[t])^2) G''[t]-7151616 ((H'[t])^3) G''[t]-83968 G[t] H'[t] ((G''[t])^2)+1480704 H[t] H'[t] ((G''[t])^2)+12288 G[t] ((H[t])^3) H'[t] (1814 G''[t]-3355 H''[t])+6018048 ((H[t])^6) H''[t]+6406144 ((G'[t])^3) H''[t]-3686400 ((G'[t])^2) H'[t] H''[t]-14639104 G'[t] ((H'[t])^2) H''[t]+11919360 ((H'[t])^3) H''[t]-19050496 G[t] H'[t] G''[t] H''[t]-17264640 H[t] H'[t] G''[t] H''[t]+1396736 ((G''[t])^2) H''[t]+17737728 G[t] H'[t] ((H''[t])^2)+17180672 H[t] H'[t] ((H''[t])^2)-2793472 G''[t] ((H''[t])^2)+1396736 ((H''[t])^3)+512 ((G[t])^6) (766240 H[t] H'[t]+65549 H''[t])+1396736 G'[t] H''[t] Derivative[3][G][t]-1396736 H'[t] H''[t] Derivative[3][G][t]+1024 G[t] ((H[t])^2) H'[t] (127062 ((G'[t])^2)+9567 Derivative[3][G][t]-19876 Derivative[3][H][t])-1024 ((G[t])^5) (903636 ((H[t])^2) H'[t]-66853 G'[t] H'[t]+19484 ((H'[t])^2)+19484 H[t] H''[t]-12181 Derivative[3][H][t])+2048 H[t] G'[t] H'[t] (723 Derivative[3][G][t]-7025 Derivative[3][H][t])+2793472 G'[t] G''[t] Derivative[3][H][t]-2793472 H'[t] G''[t] Derivative[3][H][t]-4190208 G'[t] H''[t] Derivative[3][H][t]+4190208 H'[t] H''[t] Derivative[3][H][t]+6144 ((H[t])^5) (3480 G'[t] H'[t]+5877 ((H'[t])^2)+1141 Derivative[3][H][t])+2048 G[t] ((H'[t])^2) (183915 ((H[t])^4)-64455 ((H[t])^2) G'[t]+9801 ((G'[t])^2)+11 H[t] (864 G''[t]+193 H''[t])+41 Derivative[3][G][t]+4310 Derivative[3][H][t])+1024 H[t] ((H'[t])^2) (37377 ((G'[t])^2)-1446 Derivative[3][G][t]+9112 Derivative[3][H][t])-2048 G[t] G'[t] H'[t] (41 Derivative[3][G][t]+10025 Derivative[3][H][t])+2048 H[t] G'[t] (5620 G''[t] H''[t]-6302 ((H''[t])^2)+2469 G'[t] Derivative[3][H][t])+3072 ((H[t])^3) (9780 ((G'[t])^2) H'[t]+35124 ((H'[t])^3)+H''[t] (-4054 G''[t]+4295 H''[t])-G'[t] (43940 ((H'[t])^2)+3813 Derivative[3][H][t])+H'[t] (-1304 Derivative[3][G][t]+5599 Derivative[3][H][t]))-3072 ((H[t])^4) (4 H'[t] (2445 G''[t]-7243 H''[t])+10985 G'[t] H''[t]-326 Derivative[4][H][t])+698368 ((G'[t])^2) Derivative[4][H][t]-1396736 G'[t] H'[t] Derivative[4][H][t]+698368 ((H'[t])^2) Derivative[4][H][t]-2048 G[t] H[t] H'[t] (2 G'[t] (3947 G''[t]+7449 H''[t])+41 Derivative[4][H][t])+1024 ((G[t])^4) (746314 ((H[t])^3) H'[t]+2 H'[t] (18938 G''[t]-59425 H''[t])-155054 ((H[t])^2) H''[t]+106765 G'[t] H''[t]+4 H[t] (45658 G'[t] H'[t]-77527 ((H'[t])^2)-8458 Derivative[3][H][t])+937 Derivative[4][H][t])+1024 ((G[t])^3) (127030 ((H[t])^4) H'[t]+98158 ((G'[t])^2) H'[t]+48132 ((H'[t])^3)+322782 ((H[t])^3) H''[t]+15188 G''[t] H''[t]-14547 ((H''[t])^2)+3107 H'[t] Derivative[3][G][t]-17654 H'[t] Derivative[3][H][t]+G'[t] (-145090 ((H'[t])^2)+15829 Derivative[3][H][t])+((H[t])^2) (-881262 G'[t] H'[t]+968346 ((H'[t])^2)+35204 Derivative[3][H][t])-H[t] (8 H'[t] (10673 G''[t]-20834 H''[t])+145090 G'[t] H''[t]+3107 Derivative[4][H][t]))-512 ((G[t])^2) (1082556 ((H[t])^5) H'[t]+25060 ((H'[t])^2) G''[t]+520923 ((H[t])^4) H''[t]-132111 ((G'[t])^2) H''[t]-101687 ((H'[t])^2) H''[t]-1282 H''[t] Derivative[3][G][t]-4 ((H[t])^3) (558386 G'[t] H'[t]-520923 ((H'[t])^2)-5395 Derivative[3][H][t])-2564 G''[t] Derivative[3][H][t]+3846 H''[t] Derivative[3][H][t]+2 H[t] (165900 ((G'[t])^2) H'[t]+62108 ((H'[t])^3)+(12530 G''[t]-11971 H''[t]) H''[t]+H'[t] (8762 Derivative[3][G][t]-20733 Derivative[3][H][t])+G'[t] (-228500 ((H'[t])^2)+13089 Derivative[3][H][t]))+1282 H'[t] Derivative[4][H][t]-2 G'[t] (H'[t] (13648 G''[t]-116653 H''[t])+641 Derivative[4][H][t])-2 ((H[t])^2) (H'[t] (55080 G''[t]-94478 H''[t])+114250 G'[t] H''[t]+4381 Derivative[4][H][t]))+1024 G[t] (73566 ((H[t])^5) H''[t]-9609 ((H[t])^4) Derivative[3][H][t]+2 G'[t] (10748 G''[t] H''[t]-10066 ((H''[t])^2)+5715 G'[t] Derivative[3][H][t])+((H[t])^2) (9504 G''[t] H''[t]-10309 ((H''[t])^2)+8699 G'[t] Derivative[3][H][t])-((H[t])^3) (42970 G'[t] H''[t]+3189 Derivative[4][H][t])+2 H[t] (9801 ((G'[t])^2) H''[t]+41 H''[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+82 G''[t] Derivative[3][H][t]+41 G'[t] Derivative[4][H][t]))+512 ((H[t])^2) (37377 ((G'[t])^2) H''[t]+2 G'[t] (H'[t] (32148 G''[t]-92251 H''[t])-723 Derivative[4][H][t])-3 (((H'[t])^2) (24324 G''[t]-52843 H''[t])+482 (H''[t] (Derivative[3][G][t]-3 Derivative[3][H][t])+2 G''[t] Derivative[3][H][t])-482 H'[t] Derivative[4][H][t]))))+(1/1125)1024 Γ H[t] (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[4][Ψ][t]-(1/1125)1024 Γ G[t] (937 ((G[t])^4)-3107 ((G[t])^3) H[t]+978 ((H[t])^4)+((G[t])^2) (4381 ((H[t])^2)+641 (G'[t]-H'[t]))+G[t] (-3189 ((H[t])^3)+82 H[t] (G'[t]-H'[t]))-723 ((H[t])^2) (G'[t]-H'[t])+682 (((G'[t]-H'[t]))^2)) Derivative[4][(OverBar[Ψ])][t];