Solution 5 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=(5/3*a20**2*b37)/a13**2
b73=(5/6*a20**2*b37)/a13**2
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=( - 5/2*a20**2*b37)/(a13*a8)
b63=( - 5/2*a20**2*b37)/(a13*a8)
b62=( - 5/4*a20**2*b37)/(a13*a8)
b61=(5/4*a20*b37)/a13
b60=(15/4*a20*b37)/a13
b59=(25/6*a20*b37)/a13
b58=(25/6*a20*b37)/a13
b57=(5*a20*b37)/a13
b56=(5/3*a20*b37)/a13
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=(15/8*a20**2*b37)/a8**2
b45=0
b44=(15/8*a20**2*b37)/a8**2
b43=0
b42=0
b41=( - 5/2*a20*b37)/a8
b40=( - 15/4*a20*b37)/a8
b39=( - 25/8*a20*b37)/a8
b38=( - 15/16*a20*b37)/a8
b36=(10/27*a20**2*a8*b37)/a13**3
b35=0
b34=0
b33=( - 5/6*a20**2*b37)/a13**2
b32=(5/3*a20*a8*b37)/a13**2
b31=(10/3*a20*a8*b37)/a13**2
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=0
b22=0
b21=0
b20=0
b19=( - 5/2*a20*b37)/a13
b18=(5/2*a20*b37)/a13
b17=( - 5/6*a20*b37)/a13
b16=( - 5/6*a20*b37)/a13
b15=(5/4*a8*b37)/a13
b14=( - 5/3*a8*b37)/a13
b13=(5/12*a8*b37)/a13
b12=0
b11=0
b10=0
b9=0
b8=(5/8*a20**2*b37)/a8**2
b7=0
b6=0
b5=( - 5/16*a20*b37)/a8
b4=( - 5/8*a20*b37)/a8
b3=0
b2=1/16*b37
a22=0
a21=a20
a19=0
a18=0
a17=0
a16=0
a15=( - 3/2*a13*a20)/a8
a14=( - 3/4*a13*a20)/a8
a12=(1/3*a20*a8)/a13
a11=0
a10=0
a9=0
a7= - a8
a6=0
a5=0
a4=( - 3/4*a13*a20)/a8
a3=0
a2=1/4*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,a20,a8,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
1 2 3 2 2 2
df(u,t)=(---*u *a13 *a8 - ---*u *a13 *a20 - f(v ,v )*a13*a8
4 3x 4 x x x
2 1 2 2
+ f(v,v )*a13*a8 + ---*f(v,v) *a20*a8 )/(a13*a8)
2x 3
3 3
df(v,t)=( - ---*u *a13*a20*v - ---*u *v *a13*a20 + v *a13*a8
4 2x 2 x x 3x
+ v *f(v,v)*a20*a8 + f(v,v )*a20*a8*v)/a8
x x
1 3 2 5 3
df(u,s)=(----*u *a13 *a8 *b37 - ---*u *u *a13 *a20*a8*b37
16 5x 8 3x x
5 2 2 5 2 3
- ---*u *f(v,v)*a13 *a20*a8 *b37 - ----*u *a13 *a20*a8*b37
6 3x 16 2x
5 2 2 5 3 3 2
- ---*u *f(v,v )*a13 *a20*a8 *b37 + ---*u *a13 *a20 *b37
6 2x x 8 x
5 2 2 5 2 2
+ ---*u *f(v ,v )*a13 *a20*a8 *b37 - ---*u *f(v,v )*a13 *a20*a8 *b37
2 x x x 2 x 2x
5 2 2 2 5 2 3
- ---*u *f(v,v) *a13*a20 *a8 *b37 + ----*f(v ,v )*a13 *a8 *b37
6 x 12 2x 2x
5 2 3 5 2 3
- ---*f(v ,v )*a13 *a8 *b37 + ---*f(v,v )*a13 *a8 *b37
3 x 3x 4 4x
10 3 5 2 3
+ ----*f(v,v )*f(v,v)*a13*a20*a8 *b37 + ---*f(v,v ) *a13*a20*a8 *b37
3 2x 3 x
10 3 2 3 3 2
+ ----*f(v,v) *a20 *a8 *b37)/(a13 *a8 )
27
15 2 25 2
df(v,s)=( - ----*u *a13 *a20*a8*b37*v - ----*u *v *a13 *a20*a8*b37
16 4x 8 3x x
15 2 2 15 2
+ ----*u *u *a13 *a20 *b37*v - ----*u *v *a13 *a20*a8*b37
8 2x x 4 2x 2x
5 2 15 2 2 2
- ---*u *f(v,v)*a13*a20 *a8*b37*v + ----*u *v *a13 *a20 *b37
4 2x 8 x x
5 2 5 2
- ---*u *v *a13 *a20*a8*b37 - ---*u *v *f(v,v)*a13*a20 *a8*b37
2 x 3x 2 x x
5 2 2 2
- ---*u *f(v,v )*a13*a20 *a8*b37*v + v *a13 *a8 *b37
2 x x 5x
5 2 2
+ ---*v *f(v,v)*a13*a20*a8 *b37 + 5*v *f(v,v )*a13*a20*a8 *b37
3 3x 2x x
25 2 25 2
+ ----*v *f(v ,v )*a13*a20*a8 *b37 + ----*v *f(v,v )*a13*a20*a8 *b37
6 x x x 6 x 2x
5 2 2 2 15 2
+ ---*v *f(v,v) *a20 *a8 *b37 + ----*f(v ,v )*a13*a20*a8 *b37*v
6 x 4 x 2x
5 2 5 2 2
+ ---*f(v,v )*a13*a20*a8 *b37*v + ---*f(v,v )*f(v,v)*a20 *a8 *b37*v)/
4 3x 3 x
2 2
(a13 *a8 )
df(u,t)=(1/4*df(u,x,3)*a13**2*a8 - 3/4*df(u,x)**2*a13**2*a20 - f(df(v,x),df(v,x)
)*a13*a8**2 + f(v,df(v,x,2))*a13*a8**2 + 1/3*f(v,v)**2*a20*a8**2)/(a13*a8)$
df(v,t)=( - 3/4*df(u,x,2)*a13*a20*v - 3/2*df(u,x)*df(v,x)*a13*a20 + df(v,x,3)*
a13*a8 + df(v,x)*f(v,v)*a20*a8 + f(v,df(v,x))*a20*a8*v)/a8$
df(u,s)=(1/16*df(u,x,5)*a13**3*a8**2*b37 - 5/8*df(u,x,3)*df(u,x)*a13**3*a20*a8*
b37 - 5/6*df(u,x,3)*f(v,v)*a13**2*a20*a8**2*b37 - 5/16*df(u,x,2)**2*a13**3*a20*
a8*b37 - 5/6*df(u,x,2)*f(v,df(v,x))*a13**2*a20*a8**2*b37 + 5/8*df(u,x)**3*a13**3
*a20**2*b37 + 5/2*df(u,x)*f(df(v,x),df(v,x))*a13**2*a20*a8**2*b37 - 5/2*df(u,x)*
f(v,df(v,x,2))*a13**2*a20*a8**2*b37 - 5/6*df(u,x)*f(v,v)**2*a13*a20**2*a8**2*b37
+ 5/12*f(df(v,x,2),df(v,x,2))*a13**2*a8**3*b37 - 5/3*f(df(v,x),df(v,x,3))*a13**
2*a8**3*b37 + 5/4*f(v,df(v,x,4))*a13**2*a8**3*b37 + 10/3*f(v,df(v,x,2))*f(v,v)*
a13*a20*a8**3*b37 + 5/3*f(v,df(v,x))**2*a13*a20*a8**3*b37 + 10/27*f(v,v)**3*a20
**2*a8**3*b37)/(a13**3*a8**2)$
df(v,s)=( - 15/16*df(u,x,4)*a13**2*a20*a8*b37*v - 25/8*df(u,x,3)*df(v,x)*a13**2*
a20*a8*b37 + 15/8*df(u,x,2)*df(u,x)*a13**2*a20**2*b37*v - 15/4*df(u,x,2)*df(v,x,
2)*a13**2*a20*a8*b37 - 5/4*df(u,x,2)*f(v,v)*a13*a20**2*a8*b37*v + 15/8*df(u,x)**
2*df(v,x)*a13**2*a20**2*b37 - 5/2*df(u,x)*df(v,x,3)*a13**2*a20*a8*b37 - 5/2*df(u
,x)*df(v,x)*f(v,v)*a13*a20**2*a8*b37 - 5/2*df(u,x)*f(v,df(v,x))*a13*a20**2*a8*
b37*v + df(v,x,5)*a13**2*a8**2*b37 + 5/3*df(v,x,3)*f(v,v)*a13*a20*a8**2*b37 + 5*
df(v,x,2)*f(v,df(v,x))*a13*a20*a8**2*b37 + 25/6*df(v,x)*f(df(v,x),df(v,x))*a13*
a20*a8**2*b37 + 25/6*df(v,x)*f(v,df(v,x,2))*a13*a20*a8**2*b37 + 5/6*df(v,x)*f(v,
v)**2*a20**2*a8**2*b37 + 15/4*f(df(v,x),df(v,x,2))*a13*a20*a8**2*b37*v + 5/4*f(v
,df(v,x,3))*a13*a20*a8**2*b37*v + 5/3*f(v,df(v,x))*f(v,v)*a20**2*a8**2*b37*v)/(
a13**2*a8**2)$