Solution 2 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=( - 10*a18**4*a8**2*b37)/a14**6
b73=(5/2*a18**4*a8**2*b37)/a14**6
b72=0
b71=(10*a18**4*a8*b37)/a14**5
b70=( - 25*a18**4*a8*b37)/a14**5
b69=( - 10*a18**4*a8*b37)/a14**5
b68=0
b67=0
b66=0
b65=0
b64=(10*a18**3*a8*b37)/a14**4
b63=( - 25*a18**3*a8*b37)/a14**4
b62=( - 5*a18**3*a8*b37)/a14**4
b61=( - 5*a18**2*a8*b37)/a14**3
b60=( - 5*a18**2*a8*b37)/a14**3
b59=(5*a18**2*a8*b37)/a14**3
b58=0
b57=0
b56=(5*a18**2*a8*b37)/a14**3
b55=0
b54=(5/2*a18**4*b37)/a14**4
b53=(10*a18**4*b37)/a14**4
b52=0
b51=(5*a18**3*b37)/a14**3
b50=(10*a18**3*b37)/a14**3
b49=(5*a18**3*b37)/a14**3
b48=( - 5*a18**2*b37)/a14**2
b47=( - 20*a18**2*b37)/a14**2
b46=( - 25/2*a18**2*b37)/a14**2
b45=( - 15*a18**2*b37)/a14**2
b44=( - 10*a18**2*b37)/a14**2
b43=( - 5*a18**2*b37)/a14**2
b42=0
b41=( - 5*a18*b37)/a14
b40=( - 10*a18*b37)/a14
b39=( - 15/2*a18*b37)/a14
b38=( - 5/2*a18*b37)/a14
b36=0
b35=0
b34=(10*a18**4*a8**2*b37)/a14**6
b33=(5/2*a18**4*a8**2*b37)/a14**6
b32=( - 10*a18**3*a8**2*b37)/a14**5
b31=( - 5*a18**3*a8**2*b37)/a14**5
b30=( - 5*a18**3*a8**2*b37)/a14**5
b29=0
b28=( - 10*a18**4*a8*b37)/a14**5
b27=( - 15*a18**4*a8*b37)/a14**5
b26=(5*a18**3*a8*b37)/a14**4
b25=(5*a18**3*a8*b37)/a14**4
b24=(10*a18**3*a8*b37)/a14**4
b23=0
b22=0
b21=(5*a18**2*a8*b37)/a14**3
b20=(5*a18**2*a8*b37)/a14**3
b19=(10*a18**2*a8*b37)/a14**3
b18=(5*a18**2*a8*b37)/a14**3
b17=(10*a18**2*a8*b37)/a14**3
b16=(5/2*a18**2*a8*b37)/a14**3
b15=( - 5/2*a18*a8*b37)/a14**2
b14=( - 5*a18*a8*b37)/a14**2
b13=( - 5/2*a18*a8*b37)/a14**2
b12=0
b11=( - 15/2*a18**4*b37)/a14**4
b10=0
b9=0
b8=(5/2*a18**2*b37)/a14**2
b7=(10*a18**2*b37)/a14**2
b6=(5/2*a18**2*b37)/a14**2
b5=0
b4=0
b3=0
b2= - 1/4*b37
a22=0
a21=(2*a18*a8)/a14
a20=( - a18*a8)/a14
a19=0
a17=2*a18
a16=0
a15=a14
a13=( - 1/3*a14**2)/a18
a12=0
a11=0
a10=( - 2*a18*a8)/a14
a9=( - a18*a8)/a14
a8=a8
a7=a8
a6=0
a5= - a18
a4=0
a3=0
a2=(1/6*a14**2)/a18
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
b37,a14,a18,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
1 3 2 2 2
df(u,t)=(---*u *a14 - u *f(v,v)*a18 *a8 - u *a14*a18 *u + f(v ,v )*a14*a18*a8
6 3x x x x x
2
+ f(v,v )*a14*a18*a8 - 2*f(v,v )*a18 *a8*u)/(a14*a18)
2x x
2 2 2 1 3
df(v,t)=(u *a14 *a18*v + u *v *a14 *a18 + 2*u *a14*a18 *u*v - ---*v *a14
2x x x x 3 3x
2 2 2 2
- v *f(v,v)*a18 *a8 + v *a14*a18 *u + 2*f(v,v )*a18 *a8*v)/(a14*a18)
x x x
1 6 5 3 2
df(u,s)=( - ---*u *a14 *b37 + ---*u *f(v,v)*a14 *a18 *a8*b37
4 5x 2 3x
5 4 2 2 4 2
+ ---*u *a14 *a18 *b37*u + 10*u *u *a14 *a18 *b37*u
2 3x 2x x
3 2 5 3 4 2
+ 10*u *f(v,v )*a14 *a18 *a8*b37 + ---*u *a14 *a18 *b37
2x x 2 x
3 2 3 2
+ 5*u *f(v ,v )*a14 *a18 *a8*b37 + 10*u *f(v,v )*a14 *a18 *a8*b37
x x x x 2x
2 3 5 2 4 2
+ 10*u *f(v,v )*a14 *a18 *a8*b37*u + ---*u *f(v,v) *a18 *a8 *b37
x x 2 x
4 2 15 2 4 4
- 15*u *f(v,v)*a14*a18 *a8*b37*u - ----*u *a14 *a18 *b37*u
x 2 x
5 4 4
- ---*f(v ,v )*a14 *a18*a8*b37 - 5*f(v ,v )*a14 *a18*a8*b37
2 2x 2x x 3x
3 2 3 2
+ 5*f(v ,v )*a14 *a18 *a8*b37*u - 5*f(v ,v )*f(v,v)*a14*a18 *a8 *b37
x 2x x x
2 3 2 5 4
+ 5*f(v ,v )*a14 *a18 *a8*b37*u - ---*f(v,v )*a14 *a18*a8*b37
x x 2 4x
3 2 3 2
+ 5*f(v,v )*a14 *a18 *a8*b37*u - 5*f(v,v )*f(v,v)*a14*a18 *a8 *b37
3x 2x
2 3 2 2 3 2
+ 5*f(v,v )*a14 *a18 *a8*b37*u - 10*f(v,v ) *a14*a18 *a8 *b37
2x x
4 2 4 3
+ 10*f(v,v )*f(v,v)*a18 *a8 *b37*u - 10*f(v,v )*a14*a18 *a8*b37*u )/
x x
6
a14
5 5 15 5
df(v,s)=( - ---*u *a14 *a18*b37*v - ----*u *v *a14 *a18*b37
2 4x 2 3x x
4 2 4 2
- 5*u *a14 *a18 *b37*u*v - 10*u *u *a14 *a18 *b37*v
3x 2x x
5 4 2
- 10*u *v *a14 *a18*b37 - 15*u *v *a14 *a18 *b37*u
2x 2x 2x x
2 3 3 3 2
- 5*u *f(v,v)*a14 *a18 *a8*b37*v + 5*u *a14 *a18 *b37*u *v
2x 2x
25 2 4 2 2 3 3
- ----*u *v *a14 *a18 *b37 + 10*u *a14 *a18 *b37*u*v
2 x x x
5 4 2
- 5*u *v *a14 *a18*b37 - 20*u *v *a14 *a18 *b37*u
x 3x x 2x
2 3 3 3 2
- 25*u *v *f(v,v)*a14 *a18 *a8*b37 + 5*u *v *a14 *a18 *b37*u
x x x x
2 3 4
+ 10*u *f(v,v )*a14 *a18 *a8*b37*v - 10*u *f(v,v)*a14*a18 *a8*b37*u*v
x x x
2 4 3 6
+ 10*u *a14 *a18 *b37*u *v + v *a14 *b37
x 5x
3 2 4 2 2
+ 5*v *f(v,v)*a14 *a18 *a8*b37 - 5*v *a14 *a18 *b37*u
3x 3x
3 2 5 2 4 2
+ 5*v *f(v,v )*a14 *a18 *a8*b37 + ---*v *f(v,v) *a18 *a8 *b37
x 2x 2 x
4 2 5 2 4 4
- 25*v *f(v,v)*a14*a18 *a8*b37*u + ---*v *a14 *a18 *b37*u
x 2 x
3 2 3 2
- 5*f(v ,v )*a14 *a18 *a8*b37*v - 5*f(v,v )*a14 *a18 *a8*b37*v
x 2x 3x
4 2 4 2
- 10*f(v,v )*f(v,v)*a18 *a8 *b37*v + 10*f(v,v )*a14*a18 *a8*b37*u *v)/
x x
6
a14
df(u,t)=(1/6*df(u,x,3)*a14**3 - df(u,x)*f(v,v)*a18**2*a8 - df(u,x)*a14*a18**2*u
**2 + f(df(v,x),df(v,x))*a14*a18*a8 + f(v,df(v,x,2))*a14*a18*a8 - 2*f(v,df(v,x))
*a18**2*a8*u)/(a14*a18)$
df(v,t)=(df(u,x,2)*a14**2*a18*v + df(u,x)*df(v,x)*a14**2*a18 + 2*df(u,x)*a14*a18
**2*u*v - 1/3*df(v,x,3)*a14**3 - df(v,x)*f(v,v)*a18**2*a8 + df(v,x)*a14*a18**2*u
**2 + 2*f(v,df(v,x))*a18**2*a8*v)/(a14*a18)$
df(u,s)=( - 1/4*df(u,x,5)*a14**6*b37 + 5/2*df(u,x,3)*f(v,v)*a14**3*a18**2*a8*b37
+ 5/2*df(u,x,3)*a14**4*a18**2*b37*u**2 + 10*df(u,x,2)*df(u,x)*a14**4*a18**2*b37
*u + 10*df(u,x,2)*f(v,df(v,x))*a14**3*a18**2*a8*b37 + 5/2*df(u,x)**3*a14**4*a18
**2*b37 + 5*df(u,x)*f(df(v,x),df(v,x))*a14**3*a18**2*a8*b37 + 10*df(u,x)*f(v,df(
v,x,2))*a14**3*a18**2*a8*b37 + 10*df(u,x)*f(v,df(v,x))*a14**2*a18**3*a8*b37*u +
5/2*df(u,x)*f(v,v)**2*a18**4*a8**2*b37 - 15*df(u,x)*f(v,v)*a14*a18**4*a8*b37*u**
2 - 15/2*df(u,x)*a14**2*a18**4*b37*u**4 - 5/2*f(df(v,x,2),df(v,x,2))*a14**4*a18*
a8*b37 - 5*f(df(v,x),df(v,x,3))*a14**4*a18*a8*b37 + 5*f(df(v,x),df(v,x,2))*a14**
3*a18**2*a8*b37*u - 5*f(df(v,x),df(v,x))*f(v,v)*a14*a18**3*a8**2*b37 + 5*f(df(v,
x),df(v,x))*a14**2*a18**3*a8*b37*u**2 - 5/2*f(v,df(v,x,4))*a14**4*a18*a8*b37 + 5
*f(v,df(v,x,3))*a14**3*a18**2*a8*b37*u - 5*f(v,df(v,x,2))*f(v,v)*a14*a18**3*a8**
2*b37 + 5*f(v,df(v,x,2))*a14**2*a18**3*a8*b37*u**2 - 10*f(v,df(v,x))**2*a14*a18
**3*a8**2*b37 + 10*f(v,df(v,x))*f(v,v)*a18**4*a8**2*b37*u - 10*f(v,df(v,x))*a14*
a18**4*a8*b37*u**3)/a14**6$
df(v,s)=( - 5/2*df(u,x,4)*a14**5*a18*b37*v - 15/2*df(u,x,3)*df(v,x)*a14**5*a18*
b37 - 5*df(u,x,3)*a14**4*a18**2*b37*u*v - 10*df(u,x,2)*df(u,x)*a14**4*a18**2*b37
*v - 10*df(u,x,2)*df(v,x,2)*a14**5*a18*b37 - 15*df(u,x,2)*df(v,x)*a14**4*a18**2*
b37*u - 5*df(u,x,2)*f(v,v)*a14**2*a18**3*a8*b37*v + 5*df(u,x,2)*a14**3*a18**3*
b37*u**2*v - 25/2*df(u,x)**2*df(v,x)*a14**4*a18**2*b37 + 10*df(u,x)**2*a14**3*
a18**3*b37*u*v - 5*df(u,x)*df(v,x,3)*a14**5*a18*b37 - 20*df(u,x)*df(v,x,2)*a14**
4*a18**2*b37*u - 25*df(u,x)*df(v,x)*f(v,v)*a14**2*a18**3*a8*b37 + 5*df(u,x)*df(v
,x)*a14**3*a18**3*b37*u**2 + 10*df(u,x)*f(v,df(v,x))*a14**2*a18**3*a8*b37*v - 10
*df(u,x)*f(v,v)*a14*a18**4*a8*b37*u*v + 10*df(u,x)*a14**2*a18**4*b37*u**3*v + df
(v,x,5)*a14**6*b37 + 5*df(v,x,3)*f(v,v)*a14**3*a18**2*a8*b37 - 5*df(v,x,3)*a14**
4*a18**2*b37*u**2 + 5*df(v,x)*f(v,df(v,x,2))*a14**3*a18**2*a8*b37 + 5/2*df(v,x)*
f(v,v)**2*a18**4*a8**2*b37 - 25*df(v,x)*f(v,v)*a14*a18**4*a8*b37*u**2 + 5/2*df(v
,x)*a14**2*a18**4*b37*u**4 - 5*f(df(v,x),df(v,x,2))*a14**3*a18**2*a8*b37*v - 5*f
(v,df(v,x,3))*a14**3*a18**2*a8*b37*v - 10*f(v,df(v,x))*f(v,v)*a18**4*a8**2*b37*v
+ 10*f(v,df(v,x))*a14*a18**4*a8*b37*u**2*v)/a14**6$