In[]:=
In[]:=
coefficients=Table[Coefficient[eq2,ψ[ξ],i],{i,0,6}];​​coefficients​​length=Length[coefficients]​​vars=Variables[coefficients]​​coefficients/.{c10,d10}//Simplify​​Solve[%0,{a0,a1,b1,δ}]
Out[]=
{2b1
2
c0
2
k
2
δ
-2a0c0d1
2
k
2
δ
-2b1c1d1
2
k
2
δ
+2a1
2
d1
2
k
2
δ
-2b1
2
c0
2
β
2
δ
+2a0c0d1
2
β
2
δ
+2b1c1d1
2
β
2
δ
-2a1
2
d1
2
β
2
δ
+b1
2
d1
η+
3
b1
μ,-2b1c0d1
2
k
δ+2a0
2
d1
2
k
δ+2b1c0d1
2
β
δ-2a0
2
d1
2
β
δ+6b1c0c1
2
k
2
δ
-6a0c1d1
2
k
2
δ
-6b1c0c1
2
β
2
δ
+6a0c1d1
2
β
2
δ
+2b1c0d1η+a0
2
d1
η+3a0
2
b1
μ,2b1
2
c0
2
k
δ-2a0c0d1
2
k
δ-8b1c1d1
2
k
δ+8a1
2
d1
2
k
δ-2b1
2
c0
2
β
δ+2a0c0d1
2
β
δ+8b1c1d1
2
β
δ-8a1
2
d1
2
β
δ+6b1
2
c1
2
k
2
δ
-6a1c1d1
2
k
2
δ
-6b1
2
c1
2
β
2
δ
+6a1c1d1
2
β
2
δ
+b1
2
c0
η+2a0c0d1η+2b1c1d1η+a1
2
d1
η+3
2
a0
b1μ+3a1
2
b1
μ,-2b1c0d1
2
k
+2a0
2
d1
2
k
+2b1c0d1
2
β
-2a0
2
d1
2
β
+6b1c0c1
2
k
δ+6a1c0d1
2
k
δ-12a0c1d1
2
k
δ-6b1c0c1
2
β
δ-6a1c0d1
2
β
δ+12a0c1d1
2
β
δ-2a1c0c1
2
k
2
δ
+2a0
2
c1
2
k
2
δ
+2a1c0c1
2
β
2
δ
-2a0
2
c1
2
β
2
δ
+a0
2
c0
η+2b1c0c1η+2a1c0d1η+2a0c1d1η+
3
a0
μ+6a0a1b1μ,-6b1c1d1
2
k
+6a1
2
d1
2
k
+6b1c1d1
2
β
-6a1
2
d1
2
β
+2a1
2
c0
2
k
δ-2a0c0c1
2
k
δ+8b1
2
c1
2
k
δ-8a1c1d1
2
k
δ-2a1
2
c0
2
β
δ+2a0c0c1
2
β
δ-8b1
2
c1
2
β
δ+8a1c1d1
2
β
δ+a1
2
c0
η+2a0c0c1η+b1
2
c1
η+2a1c1d1η+3
2
a0
a1μ+3
2
a1
b1μ,6a1c0d1
2
k
-6a0c1d1
2
k
-6a1c0d1
2
β
+6a0c1d1
2
β
-2a1c0c1
2
k
δ+2a0
2
c1
2
k
δ+2a1c0c1
2
β
δ-2a0
2
c1
2
β
δ+2a1c0c1η+a0
2
c1
η+3a0
2
a1
μ,2a1
2
c0
2
k
-2a0c0c1
2
k
+2b1
2
c1
2
k
-2a1c1d1
2
k
-2a1
2
c0
2
β
+2a0c0c1
2
β
-2b1
2
c1
2
β
+2a1c1d1
2
β
+a1
2
c1
η+
3
a1
μ}
Out[]=
7
Out[]=
{a0,a1,b1,c0,c1,d1,k,β,δ,η,μ}
Out[]=
{2b1
2
c0
(
2
k
-
2
β
)
2
δ
+
3
b1
μ,3a0
2
b1
μ,b1(
2
c0
(2
2
k
δ-2
2
β
δ+η)+3(
2
a0
+a1b1)μ),a0(
2
c0
η+(
2
a0
+6a1b1)μ),a1(
2
c0
(2
2
k
δ-2
2
β
δ+η)+3(
2
a0
+a1b1)μ),3a0
2
a1
μ,2a1
2
c0
(
2
k
-
2
β
)+
3
a1
μ}
Out[]=
{a00,a10,b10},a0-
c0
η
μ
,a10,b10,a0
c0
η
μ
,a10,b10,a00,a1-
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b10,δ-
η
2(
2
k
-
2
β
)
,a00,a1
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b10,δ-
η
2(
2
k
-
2
β
)
,a00,a10,b1-
c0η
2
-
2
k
μ+
2
β
μ
,δ-
η
2(
2
k
-
2
β
)
,a00,a10,b1
c0η
2
-
2
k
μ+
2
β
μ
,δ-
η
2(
2
k
-
2
β
)
,a00,a1-
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b1
-
4
2
-
2
c0

2
k
-
2
β

η
μ
+
2
2
k
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
-
2
2
β
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
24(
2
k
-
2
β
)
,δ-
η
8(
2
k
-
2
β
)
,a00,a1
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b1
4
2
-
2
c0

2
k
-
2
β

η
μ
-
2
2
k
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
+
2
2
β
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
24(
2
k
-
2
β
)
,δ-
η
8(
2
k
-
2
β
)
,a00,a1-
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b1
-
2
2
-
2
c0

2
k
-
2
β

η
μ
-
2
2
k
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
+
2
2
β
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
12(
2
k
-
2
β
)
,δ
η
4(
2
k
-
2
β
)
,a00,a1
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b1
2
2
-
2
c0

2
k
-
2
β

η
μ
+
2
2
k
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
-
2
2
β
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
12(
2
k
-
2
β
)
,δ
η
4(
2
k
-
2
β
)

​​​​a00,a1
2
-
2
c0
2
k
+
2
c0
2
β
μ
,b1
4
2
-
2
c0

2
k
-
2
β

η
μ
-
2
2
k
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
+
2
2
β
-
2
c0

2
k
-
2
β

η

2
k
-
2
β

μ
24(
2
k
-
2
β
)
,δ-
η
8(
2
k
-
2
β
)
//FullSimplify
Out[]=
a00,a1
2
2
c0
(-
2
k
+
2
β
)
μ
,b1-
2
c0
η
4
2
2
c0
(-
2
k
+
2
β
)
μ
,δ-
η
8(
2
k
-
2
β
)
