Solution 19 to problem l1o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b75=(3/2*a22**2*b2)/(a14*a2)
b74=(3*a22**2*b2)/a14**2
b73=0
b72=( - 6*a14**2*a22*b2)/a2**3
b71=( - 6*a14*a22*b2)/a2**2
b70=0
b69=0
b68=(2*a22*b2)/a2
b67=(2*a22*b2)/a2
b66=0
b65=0
b64=(6*a22*b2)/a2
b63=0
b62=(3*a22*b2)/a2
b61=(a22*b2)/a14
b60=(3*a22*b2)/a14
b59=0
b58=0
b57=0
b56=0
b55=(6*a14**5*b2)/a2**5
b54=0
b53=0
b52=0
b51=0
b50=( - 10*a14**3*b2)/a2**3
b49=( - 10*a14**3*b2)/a2**3
b48=0
b47=0
b46=0
b45=0
b44=0
b43=0
b42=0
b41=0
b40=0
b39=0
b38=(a14*b2)/a2
b37=0
b36=(3/4*a2*a22**3*b2)/a14**4
b35=( - 3*a22**2*b2)/(a14*a2)
b34=(6*a22**2*b2)/a14**2
b33=(9/2*a22**2*b2)/a14**2
b32=(6*a2*a22**2*b2)/a14**3
b31=(4*a2*a22**2*b2)/a14**3
b30=(4*a2*a22**2*b2)/a14**3
b29=(3*a14**2*a22*b2)/a2**3
b28=( - 12*a14*a22*b2)/a2**2
b27=( - 24*a14*a22*b2)/a2**2
b26=( - 6*a22*b2)/a2
b25=( - 6*a22*b2)/a2
b24=( - 12*a22*b2)/a2
b23=(a22*b2)/a2
b22=( - 2*a22*b2)/a2
b21=(2*a22*b2)/a14
b20=(6*a22*b2)/a14
b19=(8*a22*b2)/a14
b18=(8*a22*b2)/a14
b17=(12*a22*b2)/a14
b16=(4*a22*b2)/a14
b15=(a2*a22*b2)/a14**2
b14=(4*a2*a22*b2)/a14**2
b13=(3*a2*a22*b2)/a14**2
b12=0
b11=(30*a14**4*b2)/a2**4
b10=0
b9=0
b8=( - 10*a14**2*b2)/a2**2
b7=( - 40*a14**2*b2)/a2**2
b6=( - 10*a14**2*b2)/a2**2
b5=0
b4=0
b3=0
a21=(a2*a22)/a14
a20=0
a19=( - 2*a14**3)/a2**2
a18=0
a17=0
a16=0
a15=0
a13=0
a12=(1/2*a2**2*a22**2)/a14**3
a11= - a22
a10=(2*a2*a22)/a14
a9=(2*a2*a22)/a14
a8=(a2**2*a22)/a14**2
a7=(a2**2*a22)/a14**2
a6=0
a5=( - 6*a14**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,a14,a22,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
3 2 2 2 5 2
df(u,t)=(u *a14 *a2 + 2*u *f(v,v)*a14 *a2 *a22 - 6*u *a14 *u
3x x x
3 3
+ f(v ,v )*a14*a2 *a22 + f(v,v )*a14*a2 *a22
x x 2x
2 2 1 2 3 2
+ 2*f(v,v )*a14 *a2 *a22*u + ---*f(v,v) *a2 *a22
x 2
3 2 3
- f(v,v)*a14 *a2*a22*u )/(a14 *a2)
df(v,t)=
2 2 3 2 4 3
u *a14 *a2 *v + f(v,v )*a2 *a22*v + f(v,v)*a14*a2 *a22*u*v - 2*a14 *u *v
2x x
---------------------------------------------------------------------------
2
a14*a2
4 4 3 4 6 2 2
df(u,s)=(u *a14 *a2 *b2 + 4*u *f(v,v)*a14 *a2 *a22*b2 - 10*u *a14 *a2 *b2*u
5x 3x 3x
6 2 3 4
- 40*u *u *a14 *a2 *b2*u + 12*u *f(v,v )*a14 *a2 *a22*b2
2x x 2x x
4 3 3 6 2
- 2*u *f(v,v)*a14 *a2 *a22*b2*u - 10*u *a14 *a2 *b2
2x x
2 4 3 3 4
+ u *f(v,v)*a14 *a2 *a22*b2 + 8*u *f(v ,v )*a14 *a2 *a22*b2
x x x x
3 4 4 3
+ 8*u *f(v,v )*a14 *a2 *a22*b2 - 12*u *f(v,v )*a14 *a2 *a22*b2*u
x 2x x x
9 2 2 4 2 5 2 2
+ ---*u *f(v,v) *a14 *a2 *a22 *b2 - 24*u *f(v,v)*a14 *a2 *a22*b2*u
2 x x
8 4 2 5
+ 30*u *a14 *b2*u + 3*f(v ,v )*a14 *a2 *a22*b2
x 2x 2x
2 5 3 4
+ 4*f(v ,v )*a14 *a2 *a22*b2 + 6*f(v ,v )*a14 *a2 *a22*b2*u
x 3x x 2x
5 2 4 3 2
+ 4*f(v ,v )*f(v,v)*a14*a2 *a22 *b2 - 6*f(v ,v )*a14 *a2 *a22*b2*u
x x x x
2 5 3 4
+ f(v,v )*a14 *a2 *a22*b2 + 2*f(v,v )*a14 *a2 *a22*b2*u
4x 3x
5 2 4 3 2
+ 4*f(v,v )*f(v,v)*a14*a2 *a22 *b2 - 6*f(v,v )*a14 *a2 *a22*b2*u
2x 2x
2 5 2 2 4 2
+ 6*f(v,v ) *a14*a2 *a22 *b2 + 6*f(v,v )*f(v,v)*a14 *a2 *a22 *b2*u
x x
5 2 3 3 3 5 3
- 12*f(v,v )*a14 *a2 *a22*b2*u + ---*f(v,v) *a2 *a22 *b2
x 4
2 3 3 2 2 6 4 4
- 3*f(v,v) *a14 *a2 *a22 *b2*u + 3*f(v,v)*a14 *a2*a22*b2*u )/(a14
4
*a2 )
3 4 2 4
df(v,s)=(u *a14 *a2 *b2*v + 3*u *f(v,v)*a14 *a2 *a22*b2*v
4x 2x
5 2 2 2 5 2
- 10*u *a14 *a2 *b2*u *v - 10*u *a14 *a2 *b2*u*v
2x x
2 4 5
+ 6*u *f(v,v )*a14 *a2 *a22*b2*v + 3*f(v ,v )*a14*a2 *a22*b2*v
x x x 2x
2 4 5
+ 2*f(v ,v )*a14 *a2 *a22*b2*u*v + f(v,v )*a14*a2 *a22*b2*v
x x 3x
2 4 5 2
+ 2*f(v,v )*a14 *a2 *a22*b2*u*v + 3*f(v,v )*f(v,v)*a2 *a22 *b2*v
2x x
3 3 2 3 2 4 2
- 6*f(v,v )*a14 *a2 *a22*b2*u *v + ---*f(v,v) *a14*a2 *a22 *b2*u*v
x 2
4 2 3 7 5 2 5
- 6*f(v,v)*a14 *a2 *a22*b2*u *v + 6*a14 *b2*u *v)/(a14 *a2 )
df(u,t)=(df(u,x,3)*a14**3*a2**2 + 2*df(u,x)*f(v,v)*a14**2*a2**2*a22 - 6*df(u,x)*
a14**5*u**2 + f(df(v,x),df(v,x))*a14*a2**3*a22 + f(v,df(v,x,2))*a14*a2**3*a22 +
2*f(v,df(v,x))*a14**2*a2**2*a22*u + 1/2*f(v,v)**2*a2**3*a22**2 - f(v,v)*a14**3*
a2*a22*u**2)/(a14**3*a2)$
df(v,t)=(df(u,x,2)*a14**2*a2**2*v + f(v,df(v,x))*a2**3*a22*v + f(v,v)*a14*a2**2*
a22*u*v - 2*a14**4*u**3*v)/(a14*a2**2)$
df(u,s)=(df(u,x,5)*a14**4*a2**4*b2 + 4*df(u,x,3)*f(v,v)*a14**3*a2**4*a22*b2 - 10
*df(u,x,3)*a14**6*a2**2*b2*u**2 - 40*df(u,x,2)*df(u,x)*a14**6*a2**2*b2*u + 12*df
(u,x,2)*f(v,df(v,x))*a14**3*a2**4*a22*b2 - 2*df(u,x,2)*f(v,v)*a14**4*a2**3*a22*
b2*u - 10*df(u,x)**3*a14**6*a2**2*b2 + df(u,x)**2*f(v,v)*a14**4*a2**3*a22*b2 + 8
*df(u,x)*f(df(v,x),df(v,x))*a14**3*a2**4*a22*b2 + 8*df(u,x)*f(v,df(v,x,2))*a14**
3*a2**4*a22*b2 - 12*df(u,x)*f(v,df(v,x))*a14**4*a2**3*a22*b2*u + 9/2*df(u,x)*f(v
,v)**2*a14**2*a2**4*a22**2*b2 - 24*df(u,x)*f(v,v)*a14**5*a2**2*a22*b2*u**2 + 30*
df(u,x)*a14**8*b2*u**4 + 3*f(df(v,x,2),df(v,x,2))*a14**2*a2**5*a22*b2 + 4*f(df(v
,x),df(v,x,3))*a14**2*a2**5*a22*b2 + 6*f(df(v,x),df(v,x,2))*a14**3*a2**4*a22*b2*
u + 4*f(df(v,x),df(v,x))*f(v,v)*a14*a2**5*a22**2*b2 - 6*f(df(v,x),df(v,x))*a14**
4*a2**3*a22*b2*u**2 + f(v,df(v,x,4))*a14**2*a2**5*a22*b2 + 2*f(v,df(v,x,3))*a14
**3*a2**4*a22*b2*u + 4*f(v,df(v,x,2))*f(v,v)*a14*a2**5*a22**2*b2 - 6*f(v,df(v,x,
2))*a14**4*a2**3*a22*b2*u**2 + 6*f(v,df(v,x))**2*a14*a2**5*a22**2*b2 + 6*f(v,df(
v,x))*f(v,v)*a14**2*a2**4*a22**2*b2*u - 12*f(v,df(v,x))*a14**5*a2**2*a22*b2*u**3
+ 3/4*f(v,v)**3*a2**5*a22**3*b2 - 3*f(v,v)**2*a14**3*a2**3*a22**2*b2*u**2 + 3*f
(v,v)*a14**6*a2*a22*b2*u**4)/(a14**4*a2**4)$
df(v,s)=(df(u,x,4)*a14**3*a2**4*b2*v + 3*df(u,x,2)*f(v,v)*a14**2*a2**4*a22*b2*v
- 10*df(u,x,2)*a14**5*a2**2*b2*u**2*v - 10*df(u,x)**2*a14**5*a2**2*b2*u*v + 6*df
(u,x)*f(v,df(v,x))*a14**2*a2**4*a22*b2*v + 3*f(df(v,x),df(v,x,2))*a14*a2**5*a22*
b2*v + 2*f(df(v,x),df(v,x))*a14**2*a2**4*a22*b2*u*v + f(v,df(v,x,3))*a14*a2**5*
a22*b2*v + 2*f(v,df(v,x,2))*a14**2*a2**4*a22*b2*u*v + 3*f(v,df(v,x))*f(v,v)*a2**
5*a22**2*b2*v - 6*f(v,df(v,x))*a14**3*a2**3*a22*b2*u**2*v + 3/2*f(v,v)**2*a14*a2
**4*a22**2*b2*u*v - 6*f(v,v)*a14**4*a2**2*a22*b2*u**3*v + 6*a14**7*b2*u**5*v)/(
a14**2*a2**5)$