Solution 23 to problem l1o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=(15/8*a15**2*a7**2*b2)/a2**4
b72=0
b71=0
b70=(5/4*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=( - 5/2*a15**2*a7*b2)/a2**3
b62=0
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=0
b35=0
b34=(5/2*a15**2*a7**2*b2)/a2**4
b33=(15/8*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=0
a21=0
a20=( - 3/2*a15*a7)/a2
a19=0
a18=( - 1/2*a15**2)/a2
a17=0
a16=0
a14=0
a13=0
a12=0
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:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 3 3 2 2
df(u,t)=(u *a2 - ---*u *f(v,v)*a15*a7 - ---*u *a15 *u + f(v ,v )*a2*a7
3x 2 x 2 x x x
+ f(v,v )*a2*a7 - f(v,v )*a15*a7*u)/a2
2x x
3 1 2 2
u *v *a15*a2 - ---*v *f(v,v)*a15*a7 - ---*v *a15 *u
x x 2 x 2 x
df(v,t)=------------------------------------------------------
a2
4 5 2 5 2 2 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 2 2
- 10*u *u *a15 *a2 *b2*u - 6*u *f(v,v )*a15*a2 *a7*b2
2x x 2x x
5 3 2 2 2
- ---*u *a15 *a2 *b2 - 4*u *f(v ,v )*a15*a2 *a7*b2
2 x x x x
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
15 2 2 2 15 3 2
+ ----*u *f(v,v) *a15 *a7 *b2 + ----*u *f(v,v)*a15 *a7*b2*u
8 x 4 x
15 4 4 3 3
+ ----*u *a15 *b2*u + 3*f(v ,v )*a2 *a7*b2 + 4*f(v ,v )*a2 *a7*b2
8 x 2x 2x x 3x
2 5 2
- 3*f(v ,v )*a15*a2 *a7*b2*u - ---*f(v ,v )*f(v,v)*a15*a2*a7 *b2
x 2x 2 x x
3 2 2 3
- ---*f(v ,v )*a15 *a2*a7*b2*u + f(v,v )*a2 *a7*b2
2 x x 4x
2 5 2
- f(v,v )*a15*a2 *a7*b2*u - ---*f(v,v )*f(v,v)*a15*a2*a7 *b2
3x 2 2x
3 2 2 2 2
- ---*f(v,v )*a15 *a2*a7*b2*u - 3*f(v,v ) *a15*a2*a7 *b2
2 2x x
5 2 2 3 3 3 4
+ ---*f(v,v )*f(v,v)*a15 *a7 *b2*u + ---*f(v,v )*a15 *a7*b2*u )/a2
2 x 2 x
3 2 2 1 2 2 2
df(v,s)=(u *v *a15*a2 *b2 - u *v *a15 *a2 *b2*u + ---*u *v *a15 *a2 *b2
3x x 2x x 2 x x
5 2 3 3 2
- ---*u *v *f(v,v)*a15 *a2*a7*b2 - ---*u *v *a15 *a2*b2*u
2 x x 2 x x
2 2
+ v *f(v ,v )*a15*a2 *a7*b2 + v *f(v,v )*a15*a2 *a7*b2
x x x x 2x
2 15 2 2 2
- 2*v *f(v,v )*a15 *a2*a7*b2*u + ----*v *f(v,v) *a15 *a7 *b2
x x 8 x
5 3 2 3 4 4 4
+ ---*v *f(v,v)*a15 *a7*b2*u + ---*v *a15 *b2*u )/a2
4 x 8 x
df(u,t)=(df(u,x,3)*a2**2 - 3/2*df(u,x)*f(v,v)*a15*a7 - 3/2*df(u,x)*a15**2*u**2 +
f(df(v,x),df(v,x))*a2*a7 + f(v,df(v,x,2))*a2*a7 - f(v,df(v,x))*a15*a7*u)/a2$
df(v,t)=(df(u,x)*df(v,x)*a15*a2 - 3/2*df(v,x)*f(v,v)*a15*a7 - 1/2*df(v,x)*a15**2
*u**2)/a2$
df(u,s)=(df(u,x,5)*a2**4*b2 - 5/2*df(u,x,3)*f(v,v)*a15*a2**2*a7*b2 - 5/2*df(u,x,
3)*a15**2*a2**2*b2*u**2 - 10*df(u,x,2)*df(u,x)*a15**2*a2**2*b2*u - 6*df(u,x,2)*f
(v,df(v,x))*a15*a2**2*a7*b2 - 5/2*df(u,x)**3*a15**2*a2**2*b2 - 4*df(u,x)*f(df(v,
x),df(v,x))*a15*a2**2*a7*b2 - 4*df(u,x)*f(v,df(v,x,2))*a15*a2**2*a7*b2 - 3*df(u,
x)*f(v,df(v,x))*a15**2*a2*a7*b2*u + 15/8*df(u,x)*f(v,v)**2*a15**2*a7**2*b2 + 15/
4*df(u,x)*f(v,v)*a15**3*a7*b2*u**2 + 15/8*df(u,x)*a15**4*b2*u**4 + 3*f(df(v,x,2)
,df(v,x,2))*a2**3*a7*b2 + 4*f(df(v,x),df(v,x,3))*a2**3*a7*b2 - 3*f(df(v,x),df(v,
x,2))*a15*a2**2*a7*b2*u - 5/2*f(df(v,x),df(v,x))*f(v,v)*a15*a2*a7**2*b2 - 3/2*f(
df(v,x),df(v,x))*a15**2*a2*a7*b2*u**2 + f(v,df(v,x,4))*a2**3*a7*b2 - f(v,df(v,x,
3))*a15*a2**2*a7*b2*u - 5/2*f(v,df(v,x,2))*f(v,v)*a15*a2*a7**2*b2 - 3/2*f(v,df(v
,x,2))*a15**2*a2*a7*b2*u**2 - 3*f(v,df(v,x))**2*a15*a2*a7**2*b2 + 5/2*f(v,df(v,x
))*f(v,v)*a15**2*a7**2*b2*u + 3/2*f(v,df(v,x))*a15**3*a7*b2*u**3)/a2**4$
df(v,s)=(df(u,x,3)*df(v,x)*a15*a2**3*b2 - df(u,x,2)*df(v,x)*a15**2*a2**2*b2*u +
1/2*df(u,x)**2*df(v,x)*a15**2*a2**2*b2 - 5/2*df(u,x)*df(v,x)*f(v,v)*a15**2*a2*a7
*b2 - 3/2*df(u,x)*df(v,x)*a15**3*a2*b2*u**2 + df(v,x)*f(df(v,x),df(v,x))*a15*a2
**2*a7*b2 + df(v,x)*f(v,df(v,x,2))*a15*a2**2*a7*b2 - 2*df(v,x)*f(v,df(v,x))*a15
**2*a2*a7*b2*u + 15/8*df(v,x)*f(v,v)**2*a15**2*a7**2*b2 + 5/4*df(v,x)*f(v,v)*a15
**3*a7*b2*u**2 + 3/8*df(v,x)*a15**4*b2*u**4)/a2**4$