Solution 8 to problem l1o35
Expressions |
Parameters |
Relevance |
Back to problem l1o35
Expressions
The solution is given through the following expressions:
b75=0
b74=(5/9*a9**2*b37)/a13**2
b73=0
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=(25/3*a9**2*b37)/(a13*a8)
b63=(5/3*a9**2*b37)/(a13*a8)
b62=(10/3*a9**2*b37)/(a13*a8)
b61=(10/3*a9*b37)/a13
b60=(20/3*a9*b37)/a13
b59=(10/3*a9*b37)/a13
b58=(5/2*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=(15/2*a9**2*b37)/a8**2
b45=0
b44=(15*a9**2*b37)/a8**2
b43=0
b42=0
b41=(5*a9*b37)/a8
b40=(10*a9*b37)/a8
b39=(10*a9*b37)/a8
b38=(5*a9*b37)/a8
b36=0
b35=0
b34=0
b33=(5/9*a9**2*b37)/a13**2
b32=(5/6*a8*a9*b37)/a13**2
b31=(10/9*a8*a9*b37)/a13**2
b30=(5/6*a8*a9*b37)/a13**2
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=(5*a9**2*b37)/(a13*a8)
b22=0
b21=0
b20=0
b19=(25/3*a9*b37)/a13
b18=(25/6*a9*b37)/a13
b17=(25/3*a9*b37)/a13
b16=(10/3*a9*b37)/a13
b15=(5/3*a8*b37)/a13
b14=(10/3*a8*b37)/a13
b13=(5/2*a8*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=(5/2*a9**2*b37)/a8**2
b7=0
b6=0
b5=(5/2*a9*b37)/a8
b4=(5*a9*b37)/a8
b3=0
b2=b37
a22=0
a21=a9
a20=0
a19=0
a18=0
a17=0
a16=0
a15=(3*a13*a9)/a8
a14=(3*a13*a9)/a8
a12=0
a11=0
a10=0
a7=1/2*a8
a6=0
a5=0
a4=(3/2*a13*a9)/a8
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,a8,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
3 2 1 2
df(u,t)=(u *a13*a8 + ---*u *a13*a9 + u *f(v,v)*a8*a9 + ---*f(v ,v )*a8
3x 2 x x 2 x x
2
+ f(v,v )*a8 )/a8
2x
3*u *a13*a9*v + 3*u *v *a13*a9 + v *a13*a8 + f(v,v )*a8*a9*v
2x x x 3x x
df(v,t)=----------------------------------------------------------------
a8
2 2 2
df(u,s)=(u *a13 *a8 *b37 + 5*u *u *a13 *a8*a9*b37
5x 3x x
10 2 5 2 2
+ ----*u *f(v,v)*a13*a8 *a9*b37 + ---*u *a13 *a8*a9*b37
3 3x 2 2x
25 2 5 3 2 2
+ ----*u *f(v,v )*a13*a8 *a9*b37 + ---*u *a13 *a9 *b37
3 2x x 2 x
2 2 25 2
+ 5*u *f(v,v)*a13*a8*a9 *b37 + ----*u *f(v ,v )*a13*a8 *a9*b37
x 6 x x x
25 2 5 2 2 2
+ ----*u *f(v,v )*a13*a8 *a9*b37 + ---*u *f(v,v) *a8 *a9 *b37
3 x 2x 9 x
5 3 10 3
+ ---*f(v ,v )*a13*a8 *b37 + ----*f(v ,v )*a13*a8 *b37
2 2x 2x 3 x 3x
5 3 5 3
+ ---*f(v ,v )*f(v,v)*a8 *a9*b37 + ---*f(v,v )*a13*a8 *b37
6 x x 3 4x
10 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 6 x
)
2 2
df(v,s)=(5*u *a13 *a8*a9*b37*v + 10*u *v *a13 *a8*a9*b37
4x 3x x
2 2 2
+ 15*u *u *a13 *a9 *b37*v + 10*u *v *a13 *a8*a9*b37
2x x 2x 2x
10 2 15 2 2 2
+ ----*u *f(v,v)*a13*a8*a9 *b37*v + ----*u *v *a13 *a9 *b37
3 2x 2 x x
2 5 2
+ 5*u *v *a13 *a8*a9*b37 + ---*u *v *f(v,v)*a13*a8*a9 *b37
x 3x 3 x x
25 2 2 2
+ ----*u *f(v,v )*a13*a8*a9 *b37*v + v *a13 *a8 *b37
3 x x 5x
5 2 5 2
+ ---*v *f(v,v )*a13*a8 *a9*b37 + ---*v *f(v ,v )*a13*a8 *a9*b37
3 2x x 2 x x x
10 2 20 2
+ ----*v *f(v,v )*a13*a8 *a9*b37 + ----*f(v ,v )*a13*a8 *a9*b37*v
3 x 2x 3 x 2x
10 2 5 2 2
+ ----*f(v,v )*a13*a8 *a9*b37*v + ---*f(v,v )*f(v,v)*a8 *a9 *b37*v)/(
3 3x 9 x
2 2
a13 *a8 )
df(u,t)=(df(u,x,3)*a13*a8 + 3/2*df(u,x)**2*a13*a9 + df(u,x)*f(v,v)*a8*a9 + 1/2*f
(df(v,x),df(v,x))*a8**2 + f(v,df(v,x,2))*a8**2)/a8$
df(v,t)=(3*df(u,x,2)*a13*a9*v + 3*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)=(df(u,x,5)*a13**2*a8**2*b37 + 5*df(u,x,3)*df(u,x)*a13**2*a8*a9*b37 + 10/
3*df(u,x,3)*f(v,v)*a13*a8**2*a9*b37 + 5/2*df(u,x,2)**2*a13**2*a8*a9*b37 + 25/3*
df(u,x,2)*f(v,df(v,x))*a13*a8**2*a9*b37 + 5/2*df(u,x)**3*a13**2*a9**2*b37 + 5*df
(u,x)**2*f(v,v)*a13*a8*a9**2*b37 + 25/6*df(u,x)*f(df(v,x),df(v,x))*a13*a8**2*a9*
b37 + 25/3*df(u,x)*f(v,df(v,x,2))*a13*a8**2*a9*b37 + 5/9*df(u,x)*f(v,v)**2*a8**2
*a9**2*b37 + 5/2*f(df(v,x,2),df(v,x,2))*a13*a8**3*b37 + 10/3*f(df(v,x),df(v,x,3)
)*a13*a8**3*b37 + 5/6*f(df(v,x),df(v,x))*f(v,v)*a8**3*a9*b37 + 5/3*f(v,df(v,x,4)
)*a13*a8**3*b37 + 10/9*f(v,df(v,x,2))*f(v,v)*a8**3*a9*b37 + 5/6*f(v,df(v,x))**2*
a8**3*a9*b37)/(a13**2*a8**2)$
df(v,s)=(5*df(u,x,4)*a13**2*a8*a9*b37*v + 10*df(u,x,3)*df(v,x)*a13**2*a8*a9*b37
+ 15*df(u,x,2)*df(u,x)*a13**2*a9**2*b37*v + 10*df(u,x,2)*df(v,x,2)*a13**2*a8*a9*
b37 + 10/3*df(u,x,2)*f(v,v)*a13*a8*a9**2*b37*v + 15/2*df(u,x)**2*df(v,x)*a13**2*
a9**2*b37 + 5*df(u,x)*df(v,x,3)*a13**2*a8*a9*b37 + 5/3*df(u,x)*df(v,x)*f(v,v)*
a13*a8*a9**2*b37 + 25/3*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 + 5/2*df(v,x)*f(df(v
,x),df(v,x))*a13*a8**2*a9*b37 + 10/3*df(v,x)*f(v,df(v,x,2))*a13*a8**2*a9*b37 +
20/3*f(df(v,x),df(v,x,2))*a13*a8**2*a9*b37*v + 10/3*f(v,df(v,x,3))*a13*a8**2*a9*
b37*v + 5/9*f(v,df(v,x))*f(v,v)*a8**2*a9**2*b37*v)/(a13**2*a8**2)$