Solution 11 to problem l1o35
Expressions |
Parameters |
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Back to problem l1o35
Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=(5/6*a9**2*b37)/a13**2
b72=0
b71=0
b70=(5/3*a18*a9*b37)/a13**2
b69=0
b68=0
b67=0
b66=0
b65=0
b64=0
b63=0
b62=0
b61=0
b60=0
b59=(10/3*a9*b37)/a13
b58=(5/3*a9*b37)/a13
b57=(10/3*a9*b37)/a13
b56=(5/3*a9*b37)/a13
b55=0
b54=(5/6*a18**2*b37)/a13**2
b53=0
b52=0
b51=0
b50=0
b49=0
b48=(5/3*a18*b37)/a13
b47=(10/3*a18*b37)/a13
b46=(5/3*a18*b37)/a13
b45=(10/3*a18*b37)/a13
b44=0
b43=0
b42=0
b41=0
b40=0
b39=0
b38=0
b36=0
b35=0
b34=0
b33=(5/6*a9**2*b37)/a13**2
b32=0
b31=0
b30=0
b29=0
b28=0
b27=(5/3*a18*a9*b37)/a13**2
b26=0
b25=0
b24=0
b23=0
b22=0
b21=0
b20=0
b19=(10/3*a9*b37)/a13
b18=(5/3*a9*b37)/a13
b17=(10/3*a9*b37)/a13
b16=(5/3*a9*b37)/a13
b15=0
b14=0
b13=0
b12=0
b11=(5/6*a18**2*b37)/a13**2
b10=0
b9=0
b8=(5/3*a18*b37)/a13
b7=(20/3*a18*b37)/a13
b6=(5/3*a18*b37)/a13
b5=0
b4=0
b3=0
b2=b37
a22=0
a21=0
a20=a9
a19=0
a17=0
a16=0
a15=0
a14=0
a12=0
a11=0
a10=0
a8=0
a7=0
a6=0
a5=a18
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,a18,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2
df(u,t)=u *a13 + u *f(v,v)*a9 + u *a18*u
3x x x
2
df(v,t)=v *a13 + v *f(v,v)*a9 + v *a18*u
3x x x
2 5 5 2
df(u,s)=(u *a13 *b37 + ---*u *f(v,v)*a13*a9*b37 + ---*u *a13*a18*b37*u
5x 3 3x 3 3x
20 10
+ ----*u *u *a13*a18*b37*u + ----*u *f(v,v )*a13*a9*b37
3 2x x 3 2x x
5 3 5
+ ---*u *a13*a18*b37 + ---*u *f(v ,v )*a13*a9*b37
3 x 3 x x x
10 5 2 2
+ ----*u *f(v,v )*a13*a9*b37 + ---*u *f(v,v) *a9 *b37
3 x 2x 6 x
5 2 5 2 4 2
+ ---*u *f(v,v)*a18*a9*b37*u + ---*u *a18 *b37*u )/a13
3 x 6 x
10 5 2
df(v,s)=(----*u *v *a13*a18*b37*u + ---*u *v *a13*a18*b37
3 2x x 3 x x
10 2 5
+ ----*u *v *a13*a18*b37*u + v *a13 *b37 + ---*v *f(v,v)*a13*a9*b37
3 x 2x 5x 3 3x
5 2 10
+ ---*v *a13*a18*b37*u + ----*v *f(v,v )*a13*a9*b37
3 3x 3 2x x
5 10
+ ---*v *f(v ,v )*a13*a9*b37 + ----*v *f(v,v )*a13*a9*b37
3 x x x 3 x 2x
5 2 2 5 2
+ ---*v *f(v,v) *a9 *b37 + ---*v *f(v,v)*a18*a9*b37*u
6 x 3 x
5 2 4 2
+ ---*v *a18 *b37*u )/a13
6 x
df(u,t)=df(u,x,3)*a13 + df(u,x)*f(v,v)*a9 + df(u,x)*a18*u**2$
df(v,t)=df(v,x,3)*a13 + df(v,x)*f(v,v)*a9 + df(v,x)*a18*u**2$
df(u,s)=(df(u,x,5)*a13**2*b37 + 5/3*df(u,x,3)*f(v,v)*a13*a9*b37 + 5/3*df(u,x,3)*
a13*a18*b37*u**2 + 20/3*df(u,x,2)*df(u,x)*a13*a18*b37*u + 10/3*df(u,x,2)*f(v,df(
v,x))*a13*a9*b37 + 5/3*df(u,x)**3*a13*a18*b37 + 5/3*df(u,x)*f(df(v,x),df(v,x))*
a13*a9*b37 + 10/3*df(u,x)*f(v,df(v,x,2))*a13*a9*b37 + 5/6*df(u,x)*f(v,v)**2*a9**
2*b37 + 5/3*df(u,x)*f(v,v)*a18*a9*b37*u**2 + 5/6*df(u,x)*a18**2*b37*u**4)/a13**2
$
df(v,s)=(10/3*df(u,x,2)*df(v,x)*a13*a18*b37*u + 5/3*df(u,x)**2*df(v,x)*a13*a18*
b37 + 10/3*df(u,x)*df(v,x,2)*a13*a18*b37*u + 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*a18*b37*u**2 + 10/3*df(v,x,2)*f(v,df(v,x
))*a13*a9*b37 + 5/3*df(v,x)*f(df(v,x),df(v,x))*a13*a9*b37 + 10/3*df(v,x)*f(v,df(
v,x,2))*a13*a9*b37 + 5/6*df(v,x)*f(v,v)**2*a9**2*b37 + 5/3*df(v,x)*f(v,v)*a18*a9
*b37*u**2 + 5/6*df(v,x)*a18**2*b37*u**4)/a13**2$