Solution 9 to problem l1o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=(20/9*a9**2*b37)/a13**2
b73=(10/9*a9**2*b37)/a13**2
b72=0
b71=(20/9*a17*a9*b37)/a13**2
b70=(20/9*a17*a9*b37)/a13**2
b69=(20/9*a17*a9*b37)/a13**2
b68=0
b67=0
b66=0
b65=0
b64=0
b63=0
b62=0
b61=(5/3*a9*b37)/a13
b60=(10/3*a9*b37)/a13
b59=(5*a9*b37)/a13
b58=(10/3*a9*b37)/a13
b57=(5*a9*b37)/a13
b56=(5/3*a9*b37)/a13
b55=0
b54=(10/9*a17**2*b37)/a13**2
b53=(20/9*a17**2*b37)/a13**2
b52=0
b51=0
b50=0
b49=0
b48=(5/3*a17*b37)/a13
b47=(5*a17*b37)/a13
b46=(10/3*a17*b37)/a13
b45=(5*a17*b37)/a13
b44=(10/3*a17*b37)/a13
b43=(5/3*a17*b37)/a13
b42=0
b41=0
b40=0
b39=0
b38=0
b36=0
b35=0
b34=(20/9*a9**2*b37)/a13**2
b33=(10/9*a9**2*b37)/a13**2
b32=0
b31=0
b30=0
b29=0
b28=(20/9*a17*a9*b37)/a13**2
b27=(40/9*a17*a9*b37)/a13**2
b26=0
b25=0
b24=0
b23=0
b22=0
b21=(5/3*a9*b37)/a13
b20=(10/3*a9*b37)/a13
b19=(5*a9*b37)/a13
b18=(10/3*a9*b37)/a13
b17=(5*a9*b37)/a13
b16=(5/3*a9*b37)/a13
b15=0
b14=0
b13=0
b12=0
b11=(10/3*a17**2*b37)/a13**2
b10=0
b9=0
b8=(10/3*a17*b37)/a13
b7=(40/3*a17*b37)/a13
b6=(10/3*a17*b37)/a13
b5=0
b4=0
b3=0
b2=b37
a22=0
a21=a9
a20=a9
a19=0
a18=a17
a16=0
a15=0
a14=0
a12=0
a11=0
a10=a9
a8=0
a7=0
a6=0
a5=2*a17
a4=0
a3=0
a2=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,a17,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2
df(u,t)=u *a13 + u *f(v,v)*a9 + 2*u *a17*u + f(v,v )*a9*u
3x x x x
2
df(v,t)=u *a17*u*v + v *a13 + v *f(v,v)*a9 + v *a17*u + f(v,v )*a9*v
x 3x x x x
2 5 10 2
df(u,s)=(u *a13 *b37 + ---*u *f(v,v)*a13*a9*b37 + ----*u *a13*a17*b37*u
5x 3 3x 3 3x
40
+ ----*u *u *a13*a17*b37*u + 5*u *f(v,v )*a13*a9*b37
3 2x x 2x x
10 3 10
+ ----*u *a13*a17*b37 + ----*u *f(v ,v )*a13*a9*b37
3 x 3 x x x
10 2 2
+ 5*u *f(v,v )*a13*a9*b37 + ----*u *f(v,v) *a9 *b37
x 2x 9 x
40 2 10 2 4
+ ----*u *f(v,v)*a17*a9*b37*u + ----*u *a17 *b37*u
9 x 3 x
10 5
+ ----*f(v ,v )*a13*a9*b37*u + ---*f(v,v )*a13*a9*b37*u
3 x 2x 3 3x
20 2 20 3 2
+ ----*f(v,v )*f(v,v)*a9 *b37*u + ----*f(v,v )*a17*a9*b37*u )/a13
9 x 9 x
5 10
df(v,s)=(---*u *a13*a17*b37*u*v + ----*u *u *a13*a17*b37*v
3 3x 3 2x x
10 2
+ 5*u *v *a13*a17*b37*u + ----*u *v *a13*a17*b37
2x x 3 x x
20
+ 5*u *v *a13*a17*b37*u + ----*u *f(v,v)*a17*a9*b37*u*v
x 2x 9 x
20 2 3 2 5
+ ----*u *a17 *b37*u *v + v *a13 *b37 + ---*v *f(v,v)*a13*a9*b37
9 x 5x 3 3x
5 2
+ ---*v *a13*a17*b37*u + 5*v *f(v,v )*a13*a9*b37
3 3x 2x x
10
+ ----*v *f(v ,v )*a13*a9*b37 + 5*v *f(v,v )*a13*a9*b37
3 x x x x 2x
10 2 2 20 2
+ ----*v *f(v,v) *a9 *b37 + ----*v *f(v,v)*a17*a9*b37*u
9 x 9 x
10 2 4 10
+ ----*v *a17 *b37*u + ----*f(v ,v )*a13*a9*b37*v
9 x 3 x 2x
5 20 2
+ ---*f(v,v )*a13*a9*b37*v + ----*f(v,v )*f(v,v)*a9 *b37*v
3 3x 9 x
20 2 2
+ ----*f(v,v )*a17*a9*b37*u *v)/a13
9 x
df(u,t)=df(u,x,3)*a13 + df(u,x)*f(v,v)*a9 + 2*df(u,x)*a17*u**2 + f(v,df(v,x))*a9
*u$
df(v,t)=df(u,x)*a17*u*v + df(v,x,3)*a13 + df(v,x)*f(v,v)*a9 + df(v,x)*a17*u**2 +
f(v,df(v,x))*a9*v$
df(u,s)=(df(u,x,5)*a13**2*b37 + 5/3*df(u,x,3)*f(v,v)*a13*a9*b37 + 10/3*df(u,x,3)
*a13*a17*b37*u**2 + 40/3*df(u,x,2)*df(u,x)*a13*a17*b37*u + 5*df(u,x,2)*f(v,df(v,
x))*a13*a9*b37 + 10/3*df(u,x)**3*a13*a17*b37 + 10/3*df(u,x)*f(df(v,x),df(v,x))*
a13*a9*b37 + 5*df(u,x)*f(v,df(v,x,2))*a13*a9*b37 + 10/9*df(u,x)*f(v,v)**2*a9**2*
b37 + 40/9*df(u,x)*f(v,v)*a17*a9*b37*u**2 + 10/3*df(u,x)*a17**2*b37*u**4 + 10/3*
f(df(v,x),df(v,x,2))*a13*a9*b37*u + 5/3*f(v,df(v,x,3))*a13*a9*b37*u + 20/9*f(v,
df(v,x))*f(v,v)*a9**2*b37*u + 20/9*f(v,df(v,x))*a17*a9*b37*u**3)/a13**2$
df(v,s)=(5/3*df(u,x,3)*a13*a17*b37*u*v + 10/3*df(u,x,2)*df(u,x)*a13*a17*b37*v +
5*df(u,x,2)*df(v,x)*a13*a17*b37*u + 10/3*df(u,x)**2*df(v,x)*a13*a17*b37 + 5*df(u
,x)*df(v,x,2)*a13*a17*b37*u + 20/9*df(u,x)*f(v,v)*a17*a9*b37*u*v + 20/9*df(u,x)*
a17**2*b37*u**3*v + df(v,x,5)*a13**2*b37 + 5/3*df(v,x,3)*f(v,v)*a13*a9*b37 + 5/3
*df(v,x,3)*a13*a17*b37*u**2 + 5*df(v,x,2)*f(v,df(v,x))*a13*a9*b37 + 10/3*df(v,x)
*f(df(v,x),df(v,x))*a13*a9*b37 + 5*df(v,x)*f(v,df(v,x,2))*a13*a9*b37 + 10/9*df(v
,x)*f(v,v)**2*a9**2*b37 + 20/9*df(v,x)*f(v,v)*a17*a9*b37*u**2 + 10/9*df(v,x)*a17
**2*b37*u**4 + 10/3*f(df(v,x),df(v,x,2))*a13*a9*b37*v + 5/3*f(v,df(v,x,3))*a13*
a9*b37*v + 20/9*f(v,df(v,x))*f(v,v)*a9**2*b37*v + 20/9*f(v,df(v,x))*a17*a9*b37*u
**2*v)/a13**2$