Solution 6 to problem l1o35
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Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=( - 5/36*a9**2*b37)/a13**2
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=( - 5/6*a9**2*b37)/(a13*a8)
b63=(5/6*a9**2*b37)/(a13*a8)
b62=0
b61=( - 5/6*a9*b37)/a13
b60=( - 5/3*a9*b37)/a13
b59=( - 5/6*a9*b37)/a13
b58=( - 5/4*a9*b37)/a13
b57=( - 5/3*a9*b37)/a13
b56=0
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=(5/8*a9**2*b37)/a8**2
b45=0
b44=(5/4*a9**2*b37)/a8**2
b43=0
b42=0
b41=(5/2*a9*b37)/a8
b40=(5*a9*b37)/a8
b39=(15/4*a9*b37)/a8
b38=(5/4*a9*b37)/a8
b36=0
b35=0
b34=0
b33=( - 5/36*a9**2*b37)/a13**2
b32=( - 5/18*a8*a9*b37)/a13**2
b31=( - 5/9*a8*a9*b37)/a13**2
b30=( - 5/18*a8*a9*b37)/a13**2
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=(5/6*a9**2*b37)/(a13*a8)
b22=0
b21=0
b20=0
b19=(5/2*a9*b37)/a13
b18=(5/12*a9*b37)/a13
b17=(5/3*a9*b37)/a13
b16=(5/6*a9*b37)/a13
b15=(5/6*a8*b37)/a13
b14=(5/6*a8*b37)/a13
b13=(5/6*a8*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=( - 5/8*a9**2*b37)/a8**2
b7=0
b6=0
b5=( - 5/8*a9*b37)/a8
b4=( - 5/4*a9*b37)/a8
b3=0
b2= - 1/4*b37
a22=0
a21= - a9
a20=0
a19=0
a18=0
a17=0
a16=0
a15=(3/2*a13*a9)/a8
a14=(3/2*a13*a9)/a8
a12=( - 1/6*a8*a9)/a13
a11=0
a10=0
a7=1/2*a8
a6=0
a5=0
a4=( - 3/4*a13*a9)/a8
a3=0
a2= - 1/2*a13
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,a9,a8,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
1 2 3 2 2
df(u,t)=( - ---*u *a13 *a8 - ---*u *a13 *a9 + u *f(v,v)*a13*a8*a9
2 3x 4 x x
1 2 2 1 2 2
+ ---*f(v ,v )*a13*a8 + f(v,v )*a13*a8 - ---*f(v,v) *a8 *a9)/(a13
2 x x 2x 6
*a8)
3 3
---*u *a13*a9*v + ---*u *v *a13*a9 + v *a13*a8 - f(v,v )*a8*a9*v
2 2x 2 x x 3x x
df(v,t)=--------------------------------------------------------------------
a8
1 2 2 5 2
df(u,s)=( - ---*u *a13 *a8 *b37 - ---*u *u *a13 *a8*a9*b37
4 5x 4 3x x
5 2 5 2 2
+ ---*u *f(v,v)*a13*a8 *a9*b37 - ---*u *a13 *a8*a9*b37
6 3x 8 2x
5 2 5 3 2 2
+ ---*u *f(v,v )*a13*a8 *a9*b37 - ---*u *a13 *a9 *b37
3 2x x 8 x
5 2 2 5 2
+ ---*u *f(v,v)*a13*a8*a9 *b37 + ----*u *f(v ,v )*a13*a8 *a9*b37
6 x 12 x x x
5 2 5 2 2 2
+ ---*u *f(v,v )*a13*a8 *a9*b37 - ----*u *f(v,v) *a8 *a9 *b37
2 x 2x 36 x
5 3 5 3
+ ---*f(v ,v )*a13*a8 *b37 + ---*f(v ,v )*a13*a8 *b37
6 2x 2x 6 x 3x
5 3 5 3
- ----*f(v ,v )*f(v,v)*a8 *a9*b37 + ---*f(v,v )*a13*a8 *b37
18 x x 6 4x
5 3 5 2 3 2 2
- ---*f(v,v )*f(v,v)*a8 *a9*b37 - ----*f(v,v ) *a8 *a9*b37)/(a13 *a8
9 2x 18 x
)
5 2 15 2
df(v,s)=(---*u *a13 *a8*a9*b37*v + ----*u *v *a13 *a8*a9*b37
4 4x 4 3x x
5 2 2 2
+ ---*u *u *a13 *a9 *b37*v + 5*u *v *a13 *a8*a9*b37
4 2x x 2x 2x
5 2 2 2 5 2
+ ---*u *v *a13 *a9 *b37 + ---*u *v *a13 *a8*a9*b37
8 x x 2 x 3x
5 2 5 2
+ ---*u *v *f(v,v)*a13*a8*a9 *b37 - ---*u *f(v,v )*a13*a8*a9 *b37*v
6 x x 6 x x
2 2 5 2
+ v *a13 *a8 *b37 - ---*v *f(v,v )*a13*a8 *a9*b37
5x 3 2x x
5 2 5 2
- ---*v *f(v ,v )*a13*a8 *a9*b37 - ---*v *f(v,v )*a13*a8 *a9*b37
4 x x x 6 x 2x
5 2 2 2 5 2
- ----*v *f(v,v) *a8 *a9 *b37 - ---*f(v ,v )*a13*a8 *a9*b37*v
36 x 3 x 2x
5 2 2 2
- ---*f(v,v )*a13*a8 *a9*b37*v)/(a13 *a8 )
6 3x
df(u,t)=( - 1/2*df(u,x,3)*a13**2*a8 - 3/4*df(u,x)**2*a13**2*a9 + df(u,x)*f(v,v)*
a13*a8*a9 + 1/2*f(df(v,x),df(v,x))*a13*a8**2 + f(v,df(v,x,2))*a13*a8**2 - 1/6*f(
v,v)**2*a8**2*a9)/(a13*a8)$
df(v,t)=(3/2*df(u,x,2)*a13*a9*v + 3/2*df(u,x)*df(v,x)*a13*a9 + df(v,x,3)*a13*a8
- f(v,df(v,x))*a8*a9*v)/a8$
df(u,s)=( - 1/4*df(u,x,5)*a13**2*a8**2*b37 - 5/4*df(u,x,3)*df(u,x)*a13**2*a8*a9*
b37 + 5/6*df(u,x,3)*f(v,v)*a13*a8**2*a9*b37 - 5/8*df(u,x,2)**2*a13**2*a8*a9*b37
+ 5/3*df(u,x,2)*f(v,df(v,x))*a13*a8**2*a9*b37 - 5/8*df(u,x)**3*a13**2*a9**2*b37
+ 5/6*df(u,x)**2*f(v,v)*a13*a8*a9**2*b37 + 5/12*df(u,x)*f(df(v,x),df(v,x))*a13*
a8**2*a9*b37 + 5/2*df(u,x)*f(v,df(v,x,2))*a13*a8**2*a9*b37 - 5/36*df(u,x)*f(v,v)
**2*a8**2*a9**2*b37 + 5/6*f(df(v,x,2),df(v,x,2))*a13*a8**3*b37 + 5/6*f(df(v,x),
df(v,x,3))*a13*a8**3*b37 - 5/18*f(df(v,x),df(v,x))*f(v,v)*a8**3*a9*b37 + 5/6*f(v
,df(v,x,4))*a13*a8**3*b37 - 5/9*f(v,df(v,x,2))*f(v,v)*a8**3*a9*b37 - 5/18*f(v,df
(v,x))**2*a8**3*a9*b37)/(a13**2*a8**2)$
df(v,s)=(5/4*df(u,x,4)*a13**2*a8*a9*b37*v + 15/4*df(u,x,3)*df(v,x)*a13**2*a8*a9*
b37 + 5/4*df(u,x,2)*df(u,x)*a13**2*a9**2*b37*v + 5*df(u,x,2)*df(v,x,2)*a13**2*a8
*a9*b37 + 5/8*df(u,x)**2*df(v,x)*a13**2*a9**2*b37 + 5/2*df(u,x)*df(v,x,3)*a13**2
*a8*a9*b37 + 5/6*df(u,x)*df(v,x)*f(v,v)*a13*a8*a9**2*b37 - 5/6*df(u,x)*f(v,df(v,
x))*a13*a8*a9**2*b37*v + df(v,x,5)*a13**2*a8**2*b37 - 5/3*df(v,x,2)*f(v,df(v,x))
*a13*a8**2*a9*b37 - 5/4*df(v,x)*f(df(v,x),df(v,x))*a13*a8**2*a9*b37 - 5/6*df(v,x
)*f(v,df(v,x,2))*a13*a8**2*a9*b37 - 5/36*df(v,x)*f(v,v)**2*a8**2*a9**2*b37 - 5/3
*f(df(v,x),df(v,x,2))*a13*a8**2*a9*b37*v - 5/6*f(v,df(v,x,3))*a13*a8**2*a9*b37*v
)/(a13**2*a8**2)$