Solution 20 to problem l1o35
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Parameters |
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Expressions
The solution is given through the following expressions:
b75=( - 1/4*a15**3*a7**2*b2)/a2**5
b74=(1/2*a15**2*a7**2*b2)/a2**4
b73=( - 1/8*a15**2*a7**2*b2)/a2**4
b72=( - 1/4*a15**4*a7*b2)/a2**5
b71=0
b70=(1/4*a15**3*a7*b2)/a2**4
b69=0
b68=0
b67=0
b66=( - 2*a15**2*a7*b2)/a2**3
b65=0
b64=0
b63=( - 1/2*a15**2*a7*b2)/a2**3
b62=(1/2*a15**2*a7*b2)/a2**3
b61=0
b60=0
b59=(a15*a7*b2)/a2**2
b58=(a15*a7*b2)/a2**2
b57=0
b56=0
b55=0
b54=(3/8*a15**4*b2)/a2**4
b53=0
b52=0
b51=( - 3/2*a15**3*b2)/a2**3
b50=0
b49=0
b48=0
b47=0
b46=(1/2*a15**2*b2)/a2**2
b45=( - a15**2*b2)/a2**2
b44=0
b43=0
b42=0
b41=0
b40=0
b39=(a15*b2)/a2
b38=0
b37=0
b36=(1/4*a15**2*a7**3*b2)/a2**5
b35=(1/4*a15**3*a7**2*b2)/a2**5
b34=(5/2*a15**2*a7**2*b2)/a2**4
b33=(11/8*a15**2*a7**2*b2)/a2**4
b32=( - 3*a15*a7**2*b2)/a2**3
b31=( - 5/2*a15*a7**2*b2)/a2**3
b30=( - 5/2*a15*a7**2*b2)/a2**3
b29=0
b28=(3/2*a15**3*a7*b2)/a2**4
b27=(15/4*a15**3*a7*b2)/a2**4
b26=( - 3/2*a15**2*a7*b2)/a2**3
b25=( - 3/2*a15**2*a7*b2)/a2**3
b24=( - 3*a15**2*a7*b2)/a2**3
b23=0
b22=0
b21=( - a15*a7*b2)/a2**2
b20=( - 3*a15*a7*b2)/a2**2
b19=( - 4*a15*a7*b2)/a2**2
b18=( - 4*a15*a7*b2)/a2**2
b17=( - 6*a15*a7*b2)/a2**2
b16=( - 5/2*a15*a7*b2)/a2**2
b15=(a7*b2)/a2
b14=(4*a7*b2)/a2
b13=(3*a7*b2)/a2
b12=0
b11=(15/8*a15**4*b2)/a2**4
b10=0
b9=0
b8=( - 5/2*a15**2*b2)/a2**2
b7=( - 10*a15**2*b2)/a2**2
b6=( - 5/2*a15**2*b2)/a2**2
b5=0
b4=0
b3=0
a22=(1/2*a15**2*a7)/a2**2
a21=0
a20=(1/2*a15*a7)/a2
a19=0
a18=( - 1/2*a15**2)/a2
a17=0
a16=0
a14=0
a13=0
a12=( - 1/2*a15*a7**2)/a2**2
a11=0
a10=( - a15*a7)/a2
a9=( - 3/2*a15*a7)/a2
a8=a7
a6=0
a5=( - 3/2*a15**2)/a2
a4=0
a3=0
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:
b2,a7,a15,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
3 3 3 2 2 2
df(u,t)=(u *a2 - ---*u *f(v,v)*a15*a2*a7 - ---*u *a15 *a2*u + f(v ,v )*a2 *a7
3x 2 x 2 x x x
2 1 2 2 2
+ f(v,v )*a2 *a7 - f(v,v )*a15*a2*a7*u - ---*f(v,v) *a15*a7 )/a2
2x x 2
2 1 1 2 2
df(v,t)=(u *v *a15*a2 + ---*v *f(v,v)*a15*a2*a7 - ---*v *a15 *a2*u
x x 2 x 2 x
1 2 2
+ ---*f(v,v)*a15 *a7*u*v)/a2
2
5 5 3 5 2 3 2
df(u,s)=(u *a2 *b2 - ---*u *f(v,v)*a15*a2 *a7*b2 - ---*u *a15 *a2 *b2*u
5x 2 3x 2 3x
2 3 3
- 10*u *u *a15 *a2 *b2*u - 6*u *f(v,v )*a15*a2 *a7*b2
2x x 2x x
5 3 2 3 3
- ---*u *a15 *a2 *b2 - 4*u *f(v ,v )*a15*a2 *a7*b2
2 x x x x
3 2 2
- 4*u *f(v,v )*a15*a2 *a7*b2 - 3*u *f(v,v )*a15 *a2 *a7*b2*u
x 2x x x
11 2 2 2 15 3 2
+ ----*u *f(v,v) *a15 *a2*a7 *b2 + ----*u *f(v,v)*a15 *a2*a7*b2*u
8 x 4 x
15 4 4 4
+ ----*u *a15 *a2*b2*u + 3*f(v ,v )*a2 *a7*b2
8 x 2x 2x
4 3
+ 4*f(v ,v )*a2 *a7*b2 - 3*f(v ,v )*a15*a2 *a7*b2*u
x 3x x 2x
5 2 2 3 2 2 2
- ---*f(v ,v )*f(v,v)*a15*a2 *a7 *b2 - ---*f(v ,v )*a15 *a2 *a7*b2*u
2 x x 2 x x
4 3
+ f(v,v )*a2 *a7*b2 - f(v,v )*a15*a2 *a7*b2*u
4x 3x
5 2 2 3 2 2 2
- ---*f(v,v )*f(v,v)*a15*a2 *a7 *b2 - ---*f(v,v )*a15 *a2 *a7*b2*u
2 2x 2 2x
2 2 2 5 2 2
- 3*f(v,v ) *a15*a2 *a7 *b2 + ---*f(v,v )*f(v,v)*a15 *a2*a7 *b2*u
x 2 x
3 3 3 1 3 2 3
+ ---*f(v,v )*a15 *a2*a7*b2*u + ---*f(v,v) *a15 *a7 *b2
2 x 4
1 2 3 2 2 5
+ ---*f(v,v) *a15 *a7 *b2*u )/a2
4
4 2 3
df(v,s)=(u *v *a15*a2 *b2 - u *v *a15 *a2 *b2*u
3x x 2x x
1 2 2 1 2 2 3
+ ---*u *f(v,v)*a15 *a2 *a7*b2*v + ---*u *v *a15 *a2 *b2
2 2x 2 x x
1 2 2 3 3 2 2
- ---*u *v *f(v,v)*a15 *a2 *a7*b2 - ---*u *v *a15 *a2 *b2*u
2 x x 2 x x
3 3
+ v *f(v ,v )*a15*a2 *a7*b2 + v *f(v,v )*a15*a2 *a7*b2
x x x x 2x
2 2 1 2 2 2
- 2*v *f(v,v )*a15 *a2 *a7*b2*u - ---*v *f(v,v) *a15 *a2*a7 *b2
x x 8 x
1 3 2 3 4 4
+ ---*v *f(v,v)*a15 *a2*a7*b2*u + ---*v *a15 *a2*b2*u
4 x 8 x
1 2 2 1 2 3 2
+ ---*f(v,v )*f(v,v)*a15 *a2*a7 *b2*v - ---*f(v,v) *a15 *a7 *b2*u*v
2 x 4
1 4 3 5
- ---*f(v,v)*a15 *a7*b2*u *v)/a2
4
df(u,t)=(df(u,x,3)*a2**3 - 3/2*df(u,x)*f(v,v)*a15*a2*a7 - 3/2*df(u,x)*a15**2*a2*
u**2 + f(df(v,x),df(v,x))*a2**2*a7 + f(v,df(v,x,2))*a2**2*a7 - f(v,df(v,x))*a15*
a2*a7*u - 1/2*f(v,v)**2*a15*a7**2)/a2**2$
df(v,t)=(df(u,x)*df(v,x)*a15*a2**2 + 1/2*df(v,x)*f(v,v)*a15*a2*a7 - 1/2*df(v,x)*
a15**2*a2*u**2 + 1/2*f(v,v)*a15**2*a7*u*v)/a2**2$
df(u,s)=(df(u,x,5)*a2**5*b2 - 5/2*df(u,x,3)*f(v,v)*a15*a2**3*a7*b2 - 5/2*df(u,x,
3)*a15**2*a2**3*b2*u**2 - 10*df(u,x,2)*df(u,x)*a15**2*a2**3*b2*u - 6*df(u,x,2)*f
(v,df(v,x))*a15*a2**3*a7*b2 - 5/2*df(u,x)**3*a15**2*a2**3*b2 - 4*df(u,x)*f(df(v,
x),df(v,x))*a15*a2**3*a7*b2 - 4*df(u,x)*f(v,df(v,x,2))*a15*a2**3*a7*b2 - 3*df(u,
x)*f(v,df(v,x))*a15**2*a2**2*a7*b2*u + 11/8*df(u,x)*f(v,v)**2*a15**2*a2*a7**2*b2
+ 15/4*df(u,x)*f(v,v)*a15**3*a2*a7*b2*u**2 + 15/8*df(u,x)*a15**4*a2*b2*u**4 + 3
*f(df(v,x,2),df(v,x,2))*a2**4*a7*b2 + 4*f(df(v,x),df(v,x,3))*a2**4*a7*b2 - 3*f(
df(v,x),df(v,x,2))*a15*a2**3*a7*b2*u - 5/2*f(df(v,x),df(v,x))*f(v,v)*a15*a2**2*
a7**2*b2 - 3/2*f(df(v,x),df(v,x))*a15**2*a2**2*a7*b2*u**2 + f(v,df(v,x,4))*a2**4
*a7*b2 - f(v,df(v,x,3))*a15*a2**3*a7*b2*u - 5/2*f(v,df(v,x,2))*f(v,v)*a15*a2**2*
a7**2*b2 - 3/2*f(v,df(v,x,2))*a15**2*a2**2*a7*b2*u**2 - 3*f(v,df(v,x))**2*a15*a2
**2*a7**2*b2 + 5/2*f(v,df(v,x))*f(v,v)*a15**2*a2*a7**2*b2*u + 3/2*f(v,df(v,x))*
a15**3*a2*a7*b2*u**3 + 1/4*f(v,v)**3*a15**2*a7**3*b2 + 1/4*f(v,v)**2*a15**3*a7**
2*b2*u**2)/a2**5$
df(v,s)=(df(u,x,3)*df(v,x)*a15*a2**4*b2 - df(u,x,2)*df(v,x)*a15**2*a2**3*b2*u +
1/2*df(u,x,2)*f(v,v)*a15**2*a2**2*a7*b2*v + 1/2*df(u,x)**2*df(v,x)*a15**2*a2**3*
b2 - 1/2*df(u,x)*df(v,x)*f(v,v)*a15**2*a2**2*a7*b2 - 3/2*df(u,x)*df(v,x)*a15**3*
a2**2*b2*u**2 + df(v,x)*f(df(v,x),df(v,x))*a15*a2**3*a7*b2 + df(v,x)*f(v,df(v,x,
2))*a15*a2**3*a7*b2 - 2*df(v,x)*f(v,df(v,x))*a15**2*a2**2*a7*b2*u - 1/8*df(v,x)*
f(v,v)**2*a15**2*a2*a7**2*b2 + 1/4*df(v,x)*f(v,v)*a15**3*a2*a7*b2*u**2 + 3/8*df(
v,x)*a15**4*a2*b2*u**4 + 1/2*f(v,df(v,x))*f(v,v)*a15**2*a2*a7**2*b2*v - 1/4*f(v,
v)**2*a15**3*a7**2*b2*u*v - 1/4*f(v,v)*a15**4*a7*b2*u**3*v)/a2**5$