Solution 7 to problem l1o35
Expressions |
Parameters |
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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=(5*a9*b37)/a13
b59=(10/3*a9*b37)/a13
b58=(5/3*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=(10*a9**2*b37)/a8**2
b45=0
b44=(20*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=(5/9*a8*a9*b37)/a13**2
b31=(10/9*a8*a9*b37)/a13**2
b30=(5/9*a8*a9*b37)/a13**2
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=(20/3*a9**2*b37)/(a13*a8)
b22=0
b21=0
b20=0
b19=(10*a9*b37)/a13
b18=(5/3*a9*b37)/a13
b17=(20/3*a9*b37)/a13
b16=(10/3*a9*b37)/a13
b15=(5/3*a8*b37)/a13
b14=(5/3*a8*b37)/a13
b13=(5/3*a8*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=(10*a9**2*b37)/a8**2
b7=0
b6=0
b5=(5*a9*b37)/a8
b4=(10*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=0
a6=0
a5=0
a4=(3*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:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 2
u *a13*a8 + 3*u *a13*a9 + u *f(v,v)*a8*a9 + f(v,v )*a8
3x x x 2x
df(u,t)=------------------------------------------------------------
a8
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 + 10*u *u *a13 *a8*a9*b37
5x 3x x
10 2 2 2
+ ----*u *f(v,v)*a13*a8 *a9*b37 + 5*u *a13 *a8*a9*b37
3 3x 2x
20 2 3 2 2
+ ----*u *f(v,v )*a13*a8 *a9*b37 + 10*u *a13 *a9 *b37
3 2x x x
20 2 2 5 2
+ ----*u *f(v,v)*a13*a8*a9 *b37 + ---*u *f(v ,v )*a13*a8 *a9*b37
3 x 3 x x x
2 5 2 2 2
+ 10*u *f(v,v )*a13*a8 *a9*b37 + ---*u *f(v,v) *a8 *a9 *b37
x 2x 9 x
5 3 5 3
+ ---*f(v ,v )*a13*a8 *b37 + ---*f(v ,v )*a13*a8 *b37
3 2x 2x 3 x 3x
5 3 5 3
+ ---*f(v ,v )*f(v,v)*a8 *a9*b37 + ---*f(v,v )*a13*a8 *b37
9 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 9 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
+ 20*u *u *a13 *a9 *b37*v + 10*u *v *a13 *a8*a9*b37
2x x 2x 2x
10 2 2 2 2
+ ----*u *f(v,v)*a13*a8*a9 *b37*v + 10*u *v *a13 *a9 *b37
3 2x 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 3 x x x
10 2 2
+ ----*v *f(v,v )*a13*a8 *a9*b37 + 5*f(v ,v )*a13*a8 *a9*b37*v
3 x 2x 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*df(u,x)**2*a13*a9 + df(u,x)*f(v,v)*a8*a9 + 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 + 10*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*df(u,x,2)**2*a13**2*a8*a9*b37 + 20/3*df
(u,x,2)*f(v,df(v,x))*a13*a8**2*a9*b37 + 10*df(u,x)**3*a13**2*a9**2*b37 + 20/3*df
(u,x)**2*f(v,v)*a13*a8*a9**2*b37 + 5/3*df(u,x)*f(df(v,x),df(v,x))*a13*a8**2*a9*
b37 + 10*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 + 5/3*f(df(v,x,2),df(v,x,2))*a13*a8**3*b37 + 5/3*f(df(v,x),df(v,x,3))*
a13*a8**3*b37 + 5/9*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 + 5/9*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
+ 20*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 + 10*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 + 5/3*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 + 5*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)$