Solution 4 to problem l1o35
Expressions |
Parameters |
Relevance |
Back to problem l1o35
Expressions
The solution is given through the following expressions:
b75=0
b74=(560*a18**4*a8**2*b37)/a14**6
b73=(70*a18**4*a8**2*b37)/a14**6
b72=0
b71=( - 320*a18**4*a8*b37)/a14**5
b70=( - 100*a18**4*a8*b37)/a14**5
b69=( - 280*a18**4*a8*b37)/a14**5
b68=0
b67=0
b66=0
b65=0
b64=( - 320*a18**3*a8*b37)/a14**4
b63=( - 100*a18**3*a8*b37)/a14**4
b62=( - 140*a18**3*a8*b37)/a14**4
b61=(60*a18**2*a8*b37)/a14**3
b60=(140*a18**2*a8*b37)/a14**3
b59=(80*a18**2*a8*b37)/a14**3
b58=(70*a18**2*a8*b37)/a14**3
b57=(60*a18**2*a8*b37)/a14**3
b56=(10*a18**2*a8*b37)/a14**3
b55=0
b54=(30*a18**4*b37)/a14**4
b53=(120*a18**4*b37)/a14**4
b52=0
b51=(60*a18**3*b37)/a14**3
b50=(120*a18**3*b37)/a14**3
b49=(60*a18**3*b37)/a14**3
b48=( - 10*a18**2*b37)/a14**2
b47=( - 40*a18**2*b37)/a14**2
b46=( - 10*a18**2*b37)/a14**2
b45=( - 40*a18**2*b37)/a14**2
b44=0
b43=( - 20*a18**2*b37)/a14**2
b42=0
b41=( - 10*a18*b37)/a14
b40=( - 20*a18*b37)/a14
b39=( - 20*a18*b37)/a14
b38=( - 10*a18*b37)/a14
b36=0
b35=0
b34=(280*a18**4*a8**2*b37)/a14**6
b33=(70*a18**4*a8**2*b37)/a14**6
b32=( - 280*a18**3*a8**2*b37)/a14**5
b31=( - 140*a18**3*a8**2*b37)/a14**5
b30=( - 140*a18**3*a8**2*b37)/a14**5
b29=0
b28=( - 120*a18**4*a8*b37)/a14**5
b27=( - 180*a18**4*a8*b37)/a14**5
b26=(60*a18**3*a8*b37)/a14**4
b25=(60*a18**3*a8*b37)/a14**4
b24=(120*a18**3*a8*b37)/a14**4
b23=0
b22=0
b21=(20*a18**2*a8*b37)/a14**3
b20=(40*a18**2*a8*b37)/a14**3
b19=(80*a18**2*a8*b37)/a14**3
b18=(70*a18**2*a8*b37)/a14**3
b17=(120*a18**2*a8*b37)/a14**3
b16=(30*a18**2*a8*b37)/a14**3
b15=( - 10*a18*a8*b37)/a14**2
b14=( - 30*a18*a8*b37)/a14**2
b13=( - 20*a18*a8*b37)/a14**2
b12=0
b11=(30*a18**4*b37)/a14**4
b10=0
b9=0
b8=( - 10*a18**2*b37)/a14**2
b7=( - 40*a18**2*b37)/a14**2
b6=( - 10*a18**2*b37)/a14**2
b5=0
b4=0
b3=0
b2=b37
a22=0
a21=( - 4*a18*a8)/a14
a20=( - a18*a8)/a14
a19=0
a17=2*a18
a16=0
a15=a14
a13=( - 1/6*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
6 3x x x
2
+ f(v ,v )*a14*a18*a8 + f(v,v )*a14*a18*a8 - 2*f(v,v )*a18 *a8*u)/(
x x 2x x
a14*a18)
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 6 3x
2 2 2 2
- v *f(v,v)*a18 *a8 + v *a14*a18 *u - 4*f(v,v )*a18 *a8*v)/(a14*a18)
x x x
6 3 2 4 2 2
df(u,s)=(u *a14 *b37 + 30*u *f(v,v)*a14 *a18 *a8*b37 - 10*u *a14 *a18 *b37*u
5x 3x 3x
4 2 3 2
- 40*u *u *a14 *a18 *b37*u + 120*u *f(v,v )*a14 *a18 *a8*b37
2x x 2x x
3 4 2 3 2
- 10*u *a14 *a18 *b37 + 70*u *f(v ,v )*a14 *a18 *a8*b37
x x x x
3 2 2 3
+ 80*u *f(v,v )*a14 *a18 *a8*b37 + 120*u *f(v,v )*a14 *a18 *a8*b37*u
x 2x x x
2 4 2 4 2
+ 70*u *f(v,v) *a18 *a8 *b37 - 180*u *f(v,v)*a14*a18 *a8*b37*u
x x
2 4 4 4
+ 30*u *a14 *a18 *b37*u - 20*f(v ,v )*a14 *a18*a8*b37
x 2x 2x
4 3 2
- 30*f(v ,v )*a14 *a18*a8*b37 + 40*f(v ,v )*a14 *a18 *a8*b37*u
x 3x x 2x
3 2
- 140*f(v ,v )*f(v,v)*a14*a18 *a8 *b37
x x
2 3 2 4
+ 60*f(v ,v )*a14 *a18 *a8*b37*u - 10*f(v,v )*a14 *a18*a8*b37
x x 4x
3 2
+ 20*f(v,v )*a14 *a18 *a8*b37*u
3x
3 2
- 140*f(v,v )*f(v,v)*a14*a18 *a8 *b37
2x
2 3 2 2 3 2
+ 60*f(v,v )*a14 *a18 *a8*b37*u - 280*f(v,v ) *a14*a18 *a8 *b37
2x x
4 2 4 3
+ 280*f(v,v )*f(v,v)*a18 *a8 *b37*u - 120*f(v,v )*a14*a18 *a8*b37*u )/
x x
6
a14
5 5
df(v,s)=( - 10*u *a14 *a18*b37*v - 20*u *v *a14 *a18*b37
4x 3x x
4 2 5
- 20*u *a14 *a18 *b37*u*v - 20*u *v *a14 *a18*b37
3x 2x 2x
4 2 2 3
- 40*u *v *a14 *a18 *b37*u - 140*u *f(v,v)*a14 *a18 *a8*b37*v
2x x 2x
3 3 2 2 4 2
+ 60*u *a14 *a18 *b37*u *v - 10*u *v *a14 *a18 *b37
2x x x
2 3 3 5
+ 120*u *a14 *a18 *b37*u*v - 10*u *v *a14 *a18*b37
x x 3x
4 2 2 3
- 40*u *v *a14 *a18 *b37*u - 100*u *v *f(v,v)*a14 *a18 *a8*b37
x 2x x x
3 3 2 2 3
+ 60*u *v *a14 *a18 *b37*u - 320*u *f(v,v )*a14 *a18 *a8*b37*v
x x x x
4 2 4 3
- 280*u *f(v,v)*a14*a18 *a8*b37*u*v + 120*u *a14 *a18 *b37*u *v
x x
6 3 2
+ v *a14 *b37 + 10*v *f(v,v)*a14 *a18 *a8*b37
5x 3x
4 2 2 3 2
- 10*v *a14 *a18 *b37*u + 60*v *f(v,v )*a14 *a18 *a8*b37
3x 2x x
3 2 3 2
+ 70*v *f(v ,v )*a14 *a18 *a8*b37 + 80*v *f(v,v )*a14 *a18 *a8*b37
x x x x 2x
2 4 2 4 2
+ 70*v *f(v,v) *a18 *a8 *b37 - 100*v *f(v,v)*a14*a18 *a8*b37*u
x x
2 4 4 3 2
+ 30*v *a14 *a18 *b37*u + 140*f(v ,v )*a14 *a18 *a8*b37*v
x x 2x
3 2 4 2
+ 60*f(v,v )*a14 *a18 *a8*b37*v + 560*f(v,v )*f(v,v)*a18 *a8 *b37*v
3x x
4 2 6
- 320*f(v,v )*a14*a18 *a8*b37*u *v)/a14
x
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 - 1/6*df(v,x,3)*a14**3 - df(v,x)*f(v,v)*a18**2*a8 + df(v,x)*a14*a18**2*u
**2 - 4*f(v,df(v,x))*a18**2*a8*v)/(a14*a18)$
df(u,s)=(df(u,x,5)*a14**6*b37 + 30*df(u,x,3)*f(v,v)*a14**3*a18**2*a8*b37 - 10*df
(u,x,3)*a14**4*a18**2*b37*u**2 - 40*df(u,x,2)*df(u,x)*a14**4*a18**2*b37*u + 120*
df(u,x,2)*f(v,df(v,x))*a14**3*a18**2*a8*b37 - 10*df(u,x)**3*a14**4*a18**2*b37 +
70*df(u,x)*f(df(v,x),df(v,x))*a14**3*a18**2*a8*b37 + 80*df(u,x)*f(v,df(v,x,2))*
a14**3*a18**2*a8*b37 + 120*df(u,x)*f(v,df(v,x))*a14**2*a18**3*a8*b37*u + 70*df(u
,x)*f(v,v)**2*a18**4*a8**2*b37 - 180*df(u,x)*f(v,v)*a14*a18**4*a8*b37*u**2 + 30*
df(u,x)*a14**2*a18**4*b37*u**4 - 20*f(df(v,x,2),df(v,x,2))*a14**4*a18*a8*b37 -
30*f(df(v,x),df(v,x,3))*a14**4*a18*a8*b37 + 40*f(df(v,x),df(v,x,2))*a14**3*a18**
2*a8*b37*u - 140*f(df(v,x),df(v,x))*f(v,v)*a14*a18**3*a8**2*b37 + 60*f(df(v,x),
df(v,x))*a14**2*a18**3*a8*b37*u**2 - 10*f(v,df(v,x,4))*a14**4*a18*a8*b37 + 20*f(
v,df(v,x,3))*a14**3*a18**2*a8*b37*u - 140*f(v,df(v,x,2))*f(v,v)*a14*a18**3*a8**2
*b37 + 60*f(v,df(v,x,2))*a14**2*a18**3*a8*b37*u**2 - 280*f(v,df(v,x))**2*a14*a18
**3*a8**2*b37 + 280*f(v,df(v,x))*f(v,v)*a18**4*a8**2*b37*u - 120*f(v,df(v,x))*
a14*a18**4*a8*b37*u**3)/a14**6$
df(v,s)=( - 10*df(u,x,4)*a14**5*a18*b37*v - 20*df(u,x,3)*df(v,x)*a14**5*a18*b37
- 20*df(u,x,3)*a14**4*a18**2*b37*u*v - 20*df(u,x,2)*df(v,x,2)*a14**5*a18*b37 -
40*df(u,x,2)*df(v,x)*a14**4*a18**2*b37*u - 140*df(u,x,2)*f(v,v)*a14**2*a18**3*a8
*b37*v + 60*df(u,x,2)*a14**3*a18**3*b37*u**2*v - 10*df(u,x)**2*df(v,x)*a14**4*
a18**2*b37 + 120*df(u,x)**2*a14**3*a18**3*b37*u*v - 10*df(u,x)*df(v,x,3)*a14**5*
a18*b37 - 40*df(u,x)*df(v,x,2)*a14**4*a18**2*b37*u - 100*df(u,x)*df(v,x)*f(v,v)*
a14**2*a18**3*a8*b37 + 60*df(u,x)*df(v,x)*a14**3*a18**3*b37*u**2 - 320*df(u,x)*f
(v,df(v,x))*a14**2*a18**3*a8*b37*v - 280*df(u,x)*f(v,v)*a14*a18**4*a8*b37*u*v +
120*df(u,x)*a14**2*a18**4*b37*u**3*v + df(v,x,5)*a14**6*b37 + 10*df(v,x,3)*f(v,v
)*a14**3*a18**2*a8*b37 - 10*df(v,x,3)*a14**4*a18**2*b37*u**2 + 60*df(v,x,2)*f(v,
df(v,x))*a14**3*a18**2*a8*b37 + 70*df(v,x)*f(df(v,x),df(v,x))*a14**3*a18**2*a8*
b37 + 80*df(v,x)*f(v,df(v,x,2))*a14**3*a18**2*a8*b37 + 70*df(v,x)*f(v,v)**2*a18
**4*a8**2*b37 - 100*df(v,x)*f(v,v)*a14*a18**4*a8*b37*u**2 + 30*df(v,x)*a14**2*
a18**4*b37*u**4 + 140*f(df(v,x),df(v,x,2))*a14**3*a18**2*a8*b37*v + 60*f(v,df(v,
x,3))*a14**3*a18**2*a8*b37*v + 560*f(v,df(v,x))*f(v,v)*a18**4*a8**2*b37*v - 320*
f(v,df(v,x))*a14*a18**4*a8*b37*u**2*v)/a14**6$