In[]:=
ClearAll[α,eq1,coefficients,G,ξ,A,B,H,c,k,ν];​​​​dG[ξ_]:=D[G[ξ],ξ];​​ΞdG[ξ_]:=dG[ξ]
2
G[ξ]
;​​D[ΞdG[ξ_],ξ_]:=A+B
2
ΞdG[ξ]
+cΞdG[ξ];​​​​a={a0,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18,a19,a20};​​​​​​U[ξ_]:=Sum[a[[i+2]]*
i
(H+ΞdG[ξ])
,{i,p,q}]​​p=-1;q=1;​​U[ξ]​​eq1=2*(
2
ν
-
2
k
)*D[U[ξ],ξ]+2(α
2
k
2
ν
)*D[U[ξ],{ξ,2}]-3ν
2
k
*
2
D[U[ξ],ξ]
//Expand
Out[]=
a1+
a0
H+
′
G
[ξ]
2
G[ξ]
+a2H+
′
G
[ξ]
2
G[ξ]
Out[]=
4a2
2
k
2
′
G
[ξ]
3
G[ξ]
-
4a2
2
ν
2
′
G
[ξ]
3
G[ξ]
+
12a2
2
k
α
2
ν
3
′
G
[ξ]
4
G[ξ]
-
12
2
a2
2
k
ν
4
′
G
[ξ]
6
G[ξ]
-
12
2
a0
2
k
ν
4
′
G
[ξ]
6
G[ξ]
4
H+
′
G
[ξ]
2
G[ξ]
+
16a0
2
k
α
2
ν
4
′
G
[ξ]
6
G[ξ]
3
H+
′
G
[ξ]
2
G[ξ]
-
4a0
2
k
2
′
G
[ξ]
3
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
+
4a0
2
ν
2
′
G
[ξ]
3
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
-
12a0
2
k
α
2
ν
3
′
G
[ξ]
4
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
+
24a0a2
2
k
ν
4
′
G
[ξ]
6
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
-
2a2
2
k
′′
G
[ξ]
2
G[ξ]
+
2a2
2
ν
′′
G
[ξ]
2
G[ξ]
-
12a2
2
k
α
2
ν
′
G
[ξ]
′′
G
[ξ]
3
G[ξ]
+
12
2
a2
2
k
ν
2
′
G
[ξ]
′′
G
[ξ]
5
G[ξ]
+
12
2
a0
2
k
ν
2
′
G
[ξ]
′′
G
[ξ]
5
G[ξ]
4
H+
′
G
[ξ]
2
G[ξ]
-
16a0
2
k
α
2
ν
2
′
G
[ξ]
′′
G
[ξ]
5
G[ξ]
3
H+
′
G
[ξ]
2
G[ξ]
+
2a0
2
k
′′
G
[ξ]
2
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
-
2a0
2
ν
′′
G
[ξ]
2
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
+
12a0
2
k
α
2
ν
′
G
[ξ]
′′
G
[ξ]
3
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
-
24a0a2
2
k
ν
2
′
G
[ξ]
′′
G
[ξ]
5
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
-
3
2
a2
2
k
ν
2
′′
G
[ξ]
4
G[ξ]
-
3
2
a0
2
k
ν
2
′′
G
[ξ]
4
G[ξ]
4
H+
′
G
[ξ]
2
G[ξ]
+
4a0
2
k
α
2
ν
2
′′
G
[ξ]
4
G[ξ]
3
H+
′
G
[ξ]
2
G[ξ]
+
6a0a2
2
k
ν
2
′′
G
[ξ]
4
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
+
2a2
2
k
α
2
ν
(3)
G
[ξ]
2
G[ξ]
-
2a0
2
k
α
2
ν
(3)
G
[ξ]
2
G[ξ]
2
H+
′
G
[ξ]
2
G[ξ]
In[]:=
​