Solution 26 to problem l1o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=(40/9*a14**2*a7**2*b37)/a13**4
b73=(20/9*a14**2*a7**2*b37)/a13**4
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=(40/9*a14**2*a7*b37)/a13**3
b63=(40/9*a14**2*a7*b37)/a13**3
b62=(20/9*a14**2*a7*b37)/a13**3
b61=(20/9*a14*a7*b37)/a13**2
b60=(20/3*a14*a7*b37)/a13**2
b59=(70/9*a14*a7*b37)/a13**2
b58=(70/9*a14*a7*b37)/a13**2
b57=(10*a14*a7*b37)/a13**2
b56=(10/3*a14*a7*b37)/a13**2
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=(20/9*a14**2*b37)/a13**2
b45=0
b44=(20/9*a14**2*b37)/a13**2
b43=0
b42=0
b41=(10/3*a14*b37)/a13
b40=(5*a14*b37)/a13
b39=(35/9*a14*b37)/a13
b38=(10/9*a14*b37)/a13
b36=( - 80/27*a14**2*a7**3*b37)/a13**5
b35=0
b34=0
b33=( - 20/3*a14**2*a7**2*b37)/a13**4
b32=( - 10*a14*a7**2*b37)/a13**3
b31=( - 40/3*a14*a7**2*b37)/a13**3
b30=( - 10/3*a14*a7**2*b37)/a13**3
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=( - 40/9*a14**2*a7*b37)/a13**3
b22=0
b21=0
b20=0
b19=( - 80/9*a14*a7*b37)/a13**2
b18=(10/9*a14*a7*b37)/a13**2
b17=( - 20/3*a14*a7*b37)/a13**2
b16=( - 10/3*a14*a7*b37)/a13**2
b15=( - 20/9*a7*b37)/a13
b14=(10/9*a7*b37)/a13
b13=( - 5/3*a7*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=( - 20/27*a14**2*b37)/a13**2
b7=0
b6=0
b5=( - 5/6*a14*b37)/a13
b4=( - 10/9*a14*b37)/a13
b3=0
b2= - 1/9*b37
a22=0
a21=(2*a14*a7)/a13
a20=(2*a14*a7)/a13
a19=0
a18=0
a17=0
a16=0
a15=2*a14
a12=( - 2*a14*a7**2)/a13**2
a11=0
a10=0
a9=( - 2*a14*a7)/a13
a8= - 2*a7
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,a7,a14,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 2
df(u,t)=( - 2*u *f(v,v)*a13*a14*a7 + f(v ,v )*a13 *a7 - 2*f(v,v )*a13 *a7
x x x 2x
2 2 2
- 2*f(v,v) *a14*a7 )/a13
2
df(v,t)=(u *a13*a14*v + 2*u *v *a13*a14 + v *a13 + 2*v *f(v,v)*a14*a7
2x x x 3x x
+ 2*f(v,v )*a14*a7*v)/a13
x
1 5 10 4
df(u,s)=( - ---*u *a13 *b37 - ----*u *u *a13 *a14*b37
9 5x 9 3x x
10 3 5 2 4
- ----*u *f(v,v)*a13 *a14*a7*b37 - ---*u *a13 *a14*b37
3 3x 6 2x
20 3 20 3 3 2
- ----*u *f(v,v )*a13 *a14*a7*b37 - ----*u *a13 *a14 *b37
3 2x x 27 x
40 2 2 2 10 3
- ----*u *f(v,v)*a13 *a14 *a7*b37 + ----*u *f(v ,v )*a13 *a14*a7*b37
9 x 9 x x x
80 3 20 2 2 2
- ----*u *f(v,v )*a13 *a14*a7*b37 - ----*u *f(v,v) *a13*a14 *a7 *b37
9 x 2x 3 x
5 4 10 4
- ---*f(v ,v )*a13 *a7*b37 + ----*f(v ,v )*a13 *a7*b37
3 2x 2x 9 x 3x
10 2 2 20 4
- ----*f(v ,v )*f(v,v)*a13 *a14*a7 *b37 - ----*f(v,v )*a13 *a7*b37
3 x x 9 4x
40 2 2 2 2 2
- ----*f(v,v )*f(v,v)*a13 *a14*a7 *b37 - 10*f(v,v ) *a13 *a14*a7 *b37
3 2x x
80 3 2 3 5
- ----*f(v,v) *a14 *a7 *b37)/a13
27
10 3 35 3
df(v,s)=(----*u *a13 *a14*b37*v + ----*u *v *a13 *a14*b37
9 4x 9 3x x
20 2 2 3
+ ----*u *u *a13 *a14 *b37*v + 5*u *v *a13 *a14*b37
9 2x x 2x 2x
20 2 20 2 2 2
+ ----*u *f(v,v)*a13*a14 *a7*b37*v + ----*u *v *a13 *a14 *b37
9 2x 9 x x
10 3 40 2
+ ----*u *v *a13 *a14*b37 + ----*u *v *f(v,v)*a13*a14 *a7*b37
3 x 3x 9 x x
40 2 4
+ ----*u *f(v,v )*a13*a14 *a7*b37*v + v *a13 *b37
9 x x 5x
10 2 2
+ ----*v *f(v,v)*a13 *a14*a7*b37 + 10*v *f(v,v )*a13 *a14*a7*b37
3 3x 2x x
70 2 70 2
+ ----*v *f(v ,v )*a13 *a14*a7*b37 + ----*v *f(v,v )*a13 *a14*a7*b37
9 x x x 9 x 2x
20 2 2 2 20 2
+ ----*v *f(v,v) *a14 *a7 *b37 + ----*f(v ,v )*a13 *a14*a7*b37*v
9 x 3 x 2x
20 2 40 2 2
+ ----*f(v,v )*a13 *a14*a7*b37*v + ----*f(v,v )*f(v,v)*a14 *a7 *b37*v
9 3x 9 x
4
)/a13
df(u,t)=( - 2*df(u,x)*f(v,v)*a13*a14*a7 + f(df(v,x),df(v,x))*a13**2*a7 - 2*f(v,
df(v,x,2))*a13**2*a7 - 2*f(v,v)**2*a14*a7**2)/a13**2$
df(v,t)=(df(u,x,2)*a13*a14*v + 2*df(u,x)*df(v,x)*a13*a14 + df(v,x,3)*a13**2 + 2*
df(v,x)*f(v,v)*a14*a7 + 2*f(v,df(v,x))*a14*a7*v)/a13$
df(u,s)=( - 1/9*df(u,x,5)*a13**5*b37 - 10/9*df(u,x,3)*df(u,x)*a13**4*a14*b37 -
10/3*df(u,x,3)*f(v,v)*a13**3*a14*a7*b37 - 5/6*df(u,x,2)**2*a13**4*a14*b37 - 20/3
*df(u,x,2)*f(v,df(v,x))*a13**3*a14*a7*b37 - 20/27*df(u,x)**3*a13**3*a14**2*b37 -
40/9*df(u,x)**2*f(v,v)*a13**2*a14**2*a7*b37 + 10/9*df(u,x)*f(df(v,x),df(v,x))*
a13**3*a14*a7*b37 - 80/9*df(u,x)*f(v,df(v,x,2))*a13**3*a14*a7*b37 - 20/3*df(u,x)
*f(v,v)**2*a13*a14**2*a7**2*b37 - 5/3*f(df(v,x,2),df(v,x,2))*a13**4*a7*b37 + 10/
9*f(df(v,x),df(v,x,3))*a13**4*a7*b37 - 10/3*f(df(v,x),df(v,x))*f(v,v)*a13**2*a14
*a7**2*b37 - 20/9*f(v,df(v,x,4))*a13**4*a7*b37 - 40/3*f(v,df(v,x,2))*f(v,v)*a13
**2*a14*a7**2*b37 - 10*f(v,df(v,x))**2*a13**2*a14*a7**2*b37 - 80/27*f(v,v)**3*
a14**2*a7**3*b37)/a13**5$
df(v,s)=(10/9*df(u,x,4)*a13**3*a14*b37*v + 35/9*df(u,x,3)*df(v,x)*a13**3*a14*b37
+ 20/9*df(u,x,2)*df(u,x)*a13**2*a14**2*b37*v + 5*df(u,x,2)*df(v,x,2)*a13**3*a14
*b37 + 20/9*df(u,x,2)*f(v,v)*a13*a14**2*a7*b37*v + 20/9*df(u,x)**2*df(v,x)*a13**
2*a14**2*b37 + 10/3*df(u,x)*df(v,x,3)*a13**3*a14*b37 + 40/9*df(u,x)*df(v,x)*f(v,
v)*a13*a14**2*a7*b37 + 40/9*df(u,x)*f(v,df(v,x))*a13*a14**2*a7*b37*v + df(v,x,5)
*a13**4*b37 + 10/3*df(v,x,3)*f(v,v)*a13**2*a14*a7*b37 + 10*df(v,x,2)*f(v,df(v,x)
)*a13**2*a14*a7*b37 + 70/9*df(v,x)*f(df(v,x),df(v,x))*a13**2*a14*a7*b37 + 70/9*
df(v,x)*f(v,df(v,x,2))*a13**2*a14*a7*b37 + 20/9*df(v,x)*f(v,v)**2*a14**2*a7**2*
b37 + 20/3*f(df(v,x),df(v,x,2))*a13**2*a14*a7*b37*v + 20/9*f(v,df(v,x,3))*a13**2
*a14*a7*b37*v + 40/9*f(v,df(v,x))*f(v,v)*a14**2*a7**2*b37*v)/a13**4$