Solution 27 to problem l1o35
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Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=( - 5/27*a14**2*a8**2*b37)/a13**4
b73=( - 5/27*a14**2*a8**2*b37)/a13**4
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=( - 5/9*a14**2*a8*b37)/a13**3
b63=(5/9*a14**2*a8*b37)/a13**3
b62=0
b61=( - 10/9*a14*a8*b37)/a13**2
b60=( - 25/9*a14*a8*b37)/a13**2
b59=( - 10/9*a14*a8*b37)/a13**2
b58=( - 5/3*a14*a8*b37)/a13**2
b57=( - 5/3*a14*a8*b37)/a13**2
b56=0
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=(5/9*a14**2*b37)/a13**2
b45=0
b44=(10/9*a14**2*b37)/a13**2
b43=0
b42=0
b41=(5/3*a14*b37)/a13
b40=(10/3*a14*b37)/a13
b39=(25/9*a14*b37)/a13
b38=(10/9*a14*b37)/a13
b36=0
b35=0
b34=0
b33=( - 10/27*a14**2*a8**2*b37)/a13**4
b32=( - 5/27*a14*a8**2*b37)/a13**3
b31=( - 40/27*a14*a8**2*b37)/a13**3
b30=( - 25/27*a14*a8**2*b37)/a13**3
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=(10/9*a14**2*a8*b37)/a13**3
b22=0
b21=0
b20=0
b19=(10/3*a14*a8*b37)/a13**2
b18=(5/9*a14*a8*b37)/a13**2
b17=(10/9*a14*a8*b37)/a13**2
b16=(10/9*a14*a8*b37)/a13**2
b15=(10/9*a8*b37)/a13
b14=(5/9*a8*b37)/a13
b13=(10/9*a8*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=( - 5/27*a14**2*b37)/a13**2
b7=0
b6=0
b5=0
b4=( - 5/9*a14*b37)/a13
b3=0
b2= - 1/9*b37
a22=0
a21=( - a14*a8)/a13
a20=0
a19=0
a18=0
a17=0
a16=0
a15=a14
a12=( - 1/3*a14*a8**2)/a13**2
a11=0
a10=0
a9=(a14*a8)/a13
a7=0
a6=0
a5=0
a4=0
a3=0
a2=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:
b37,a14,a8,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 1 2 2
u *f(v,v)*a13*a14*a8 + f(v,v )*a13 *a8 - ---*f(v,v) *a14*a8
x 2x 3
df(u,t)=---------------------------------------------------------------
2
a13
2
u *a13*a14*v + u *v *a13*a14 + v *a13 - f(v,v )*a14*a8*v
2x x x 3x x
df(v,t)=-------------------------------------------------------------
a13
1 4 5 3
df(u,s)=( - ---*u *a13 *b37 - ---*u *u *a13 *a14*b37
9 5x 9 3x x
10 2 10 2
+ ----*u *f(v,v)*a13 *a14*a8*b37 + ----*u *f(v,v )*a13 *a14*a8*b37
9 3x 9 2x x
5 3 2 2 10 2 2
- ----*u *a13 *a14 *b37 + ----*u *f(v,v)*a13*a14 *a8*b37
27 x 9 x
5 2 10 2
+ ---*u *f(v ,v )*a13 *a14*a8*b37 + ----*u *f(v,v )*a13 *a14*a8*b37
9 x x x 3 x 2x
10 2 2 2 10 3
- ----*u *f(v,v) *a14 *a8 *b37 + ----*f(v ,v )*a13 *a8*b37
27 x 9 2x 2x
5 3 25 2
+ ---*f(v ,v )*a13 *a8*b37 - ----*f(v ,v )*f(v,v)*a13*a14*a8 *b37
9 x 3x 27 x x
10 3 40 2
+ ----*f(v,v )*a13 *a8*b37 - ----*f(v,v )*f(v,v)*a13*a14*a8 *b37
9 4x 27 2x
5 2 2 4
- ----*f(v,v ) *a13*a14*a8 *b37)/a13
27 x
10 3 25 3
df(v,s)=(----*u *a13 *a14*b37*v + ----*u *v *a13 *a14*b37
9 4x 9 3x x
10 2 2 10 3
+ ----*u *u *a13 *a14 *b37*v + ----*u *v *a13 *a14*b37
9 2x x 3 2x 2x
5 2 2 2 5 3
+ ---*u *v *a13 *a14 *b37 + ---*u *v *a13 *a14*b37
9 x x 3 x 3x
5 2 5 2
+ ---*u *v *f(v,v)*a13*a14 *a8*b37 - ---*u *f(v,v )*a13*a14 *a8*b37*v
9 x x 9 x x
4 5 2
+ v *a13 *b37 - ---*v *f(v,v )*a13 *a14*a8*b37
5x 3 2x x
5 2 10 2
- ---*v *f(v ,v )*a13 *a14*a8*b37 - ----*v *f(v,v )*a13 *a14*a8*b37
3 x x x 9 x 2x
5 2 2 2 25 2
- ----*v *f(v,v) *a14 *a8 *b37 - ----*f(v ,v )*a13 *a14*a8*b37*v
27 x 9 x 2x
10 2 5 2 2
- ----*f(v,v )*a13 *a14*a8*b37*v - ----*f(v,v )*f(v,v)*a14 *a8 *b37*v
9 3x 27 x
4
)/a13
df(u,t)=(df(u,x)*f(v,v)*a13*a14*a8 + f(v,df(v,x,2))*a13**2*a8 - 1/3*f(v,v)**2*
a14*a8**2)/a13**2$
df(v,t)=(df(u,x,2)*a13*a14*v + df(u,x)*df(v,x)*a13*a14 + df(v,x,3)*a13**2 - f(v,
df(v,x))*a14*a8*v)/a13$
df(u,s)=( - 1/9*df(u,x,5)*a13**4*b37 - 5/9*df(u,x,3)*df(u,x)*a13**3*a14*b37 + 10
/9*df(u,x,3)*f(v,v)*a13**2*a14*a8*b37 + 10/9*df(u,x,2)*f(v,df(v,x))*a13**2*a14*
a8*b37 - 5/27*df(u,x)**3*a13**2*a14**2*b37 + 10/9*df(u,x)**2*f(v,v)*a13*a14**2*
a8*b37 + 5/9*df(u,x)*f(df(v,x),df(v,x))*a13**2*a14*a8*b37 + 10/3*df(u,x)*f(v,df(
v,x,2))*a13**2*a14*a8*b37 - 10/27*df(u,x)*f(v,v)**2*a14**2*a8**2*b37 + 10/9*f(df
(v,x,2),df(v,x,2))*a13**3*a8*b37 + 5/9*f(df(v,x),df(v,x,3))*a13**3*a8*b37 - 25/
27*f(df(v,x),df(v,x))*f(v,v)*a13*a14*a8**2*b37 + 10/9*f(v,df(v,x,4))*a13**3*a8*
b37 - 40/27*f(v,df(v,x,2))*f(v,v)*a13*a14*a8**2*b37 - 5/27*f(v,df(v,x))**2*a13*
a14*a8**2*b37)/a13**4$
df(v,s)=(10/9*df(u,x,4)*a13**3*a14*b37*v + 25/9*df(u,x,3)*df(v,x)*a13**3*a14*b37
+ 10/9*df(u,x,2)*df(u,x)*a13**2*a14**2*b37*v + 10/3*df(u,x,2)*df(v,x,2)*a13**3*
a14*b37 + 5/9*df(u,x)**2*df(v,x)*a13**2*a14**2*b37 + 5/3*df(u,x)*df(v,x,3)*a13**
3*a14*b37 + 5/9*df(u,x)*df(v,x)*f(v,v)*a13*a14**2*a8*b37 - 5/9*df(u,x)*f(v,df(v,
x))*a13*a14**2*a8*b37*v + df(v,x,5)*a13**4*b37 - 5/3*df(v,x,2)*f(v,df(v,x))*a13
**2*a14*a8*b37 - 5/3*df(v,x)*f(df(v,x),df(v,x))*a13**2*a14*a8*b37 - 10/9*df(v,x)
*f(v,df(v,x,2))*a13**2*a14*a8*b37 - 5/27*df(v,x)*f(v,v)**2*a14**2*a8**2*b37 - 25
/9*f(df(v,x),df(v,x,2))*a13**2*a14*a8*b37*v - 10/9*f(v,df(v,x,3))*a13**2*a14*a8*
b37*v - 5/27*f(v,df(v,x))*f(v,v)*a14**2*a8**2*b37*v)/a13**4$