Solution 25 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=( - 10/9*a20**6*b37)/(a18**2*a8**4)
b73=(5/9*a20**6*b37)/(a18**2*a8**4)
b72=0
b71=(5/9*a20**5*b37)/(a18*a8**4)
b70=(25/9*a20**5*b37)/(a18*a8**4)
b69=(20/9*a20**5*b37)/(a18*a8**4)
b68=0
b67=0
b66=0
b65=0
b64=( - 5/9*a20**4*b37)/(a18*a8**3)
b63=( - 25/9*a20**4*b37)/(a18*a8**3)
b62=( - 10/9*a20**4*b37)/(a18*a8**3)
b61=(10/9*a20**3*b37)/(a18*a8**2)
b60=(5/3*a20**3*b37)/(a18*a8**2)
b59=( - 20/9*a20**3*b37)/(a18*a8**2)
b58=( - 5/9*a20**3*b37)/(a18*a8**2)
b57=( - 5/3*a20**3*b37)/(a18*a8**2)
b56=( - 5/3*a20**3*b37)/(a18*a8**2)
b55=0
b54=(5/9*a20**4*b37)/a8**4
b53=(20/9*a20**4*b37)/a8**4
b52=0
b51=( - 10/9*a20**3*b37)/a8**3
b50=( - 20/9*a20**3*b37)/a8**3
b49=( - 10/9*a20**3*b37)/a8**3
b48=( - 5/3*a20**2*b37)/a8**2
b47=( - 20/3*a20**2*b37)/a8**2
b46=( - 5*a20**2*b37)/a8**2
b45=( - 50/9*a20**2*b37)/a8**2
b44=( - 50/9*a20**2*b37)/a8**2
b43=( - 20/9*a20**2*b37)/a8**2
b42=0
b41=(5/3*a20*b37)/a8
b40=(10/3*a20*b37)/a8
b39=(25/9*a20*b37)/a8
b38=(10/9*a20*b37)/a8
b36=0
b35=0
b34=(20/9*a20**6*b37)/(a18**2*a8**4)
b33=(5/9*a20**6*b37)/(a18**2*a8**4)
b32=(20/9*a20**5*b37)/(a18**2*a8**3)
b31=(10/9*a20**5*b37)/(a18**2*a8**3)
b30=(10/9*a20**5*b37)/(a18**2*a8**3)
b29=0
b28=(20/9*a20**5*b37)/(a18*a8**4)
b27=(10/3*a20**5*b37)/(a18*a8**4)
b26=(10/9*a20**4*b37)/(a18*a8**3)
b25=(10/9*a20**4*b37)/(a18*a8**3)
b24=(20/9*a20**4*b37)/(a18*a8**3)
b23=0
b22=0
b21=( - 20/9*a20**3*b37)/(a18*a8**2)
b20=( - 10/3*a20**3*b37)/(a18*a8**2)
b19=( - 10/3*a20**3*b37)/(a18*a8**2)
b18=( - 5/3*a20**3*b37)/(a18*a8**2)
b17=( - 20/9*a20**3*b37)/(a18*a8**2)
b16=( - 5/9*a20**3*b37)/(a18*a8**2)
b15=( - 10/9*a20**2*b37)/(a18*a8)
b14=( - 25/9*a20**2*b37)/(a18*a8)
b13=( - 5/3*a20**2*b37)/(a18*a8)
b12=0
b11=( - 5/9*a20**4*b37)/a8**4
b10=0
b9=0
b8=(5/9*a20**2*b37)/a8**2
b7=(20/9*a20**2*b37)/a8**2
b6=(5/9*a20**2*b37)/a8**2
b5=(5/9*a20*b37)/a8
b4=(5/9*a20*b37)/a8
b3=0
b2= - 1/9*b37
a22=0
a21= - a20
a19=0
a17=2*a18
a16=0
a15=( - a18*a8)/a20
a14=( - a18*a8)/a20
a13=( - a18*a8**2)/a20**2
a12=0
a11=0
a10=2*a20
a9=a20
a8=a8
a7=a8
a6=0
a5=0
a4=0
a3=0
a2=0
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,a18,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
df(u,t)=u *f(v,v)*a20 + f(v ,v )*a8 + f(v,v )*a8 + 2*f(v,v )*a20*u
x x x 2x x
2
df(v,t)=( - u *a18*a20*a8*v - u *v *a18*a20*a8 + 2*u *a18*a20 *u*v
2x x x x
2 3 2 2 3 2
- v *a18*a8 + v *f(v,v)*a20 + v *a18*a20 *u - f(v,v )*a20 *v)/a20
3x x x x
1 2 4 5 2 3
df(u,s)=( - ---*u *a18 *a8 *b37 + ---*u *u *a18 *a20*a8 *b37
9 5x 9 3x x
5 3 2 5 2 2 2 2
- ---*u *f(v,v)*a18*a20 *a8 *b37 + ---*u *a18 *a20 *a8 *b37*u
9 3x 9 3x
5 2 2 3 20 2 2 2
+ ---*u *a18 *a20*a8 *b37 + ----*u *u *a18 *a20 *a8 *b37*u
9 2x 9 2x x
20 3 2 5 3 2 2 2
- ----*u *f(v,v )*a18*a20 *a8 *b37 + ---*u *a18 *a20 *a8 *b37
9 2x x 9 x
5 3 2 10 3 2
- ---*u *f(v ,v )*a18*a20 *a8 *b37 - ----*u *f(v,v )*a18*a20 *a8 *b37
3 x x x 3 x 2x
20 4 5 2 6
+ ----*u *f(v,v )*a18*a20 *a8*b37*u + ---*u *f(v,v) *a20 *b37
9 x x 9 x
10 5 2 5 2 4 4
+ ----*u *f(v,v)*a18*a20 *b37*u - ---*u *a18 *a20 *b37*u
3 x 9 x
5 2 3 25 2 3
- ---*f(v ,v )*a18*a20 *a8 *b37 - ----*f(v ,v )*a18*a20 *a8 *b37
3 2x 2x 9 x 3x
10 3 2 10 5
- ----*f(v ,v )*a18*a20 *a8 *b37*u + ----*f(v ,v )*f(v,v)*a20 *a8*b37
3 x 2x 9 x x
10 4 2 10 2 3
+ ----*f(v ,v )*a18*a20 *a8*b37*u - ----*f(v,v )*a18*a20 *a8 *b37
9 x x 9 4x
20 3 2 10 5
- ----*f(v,v )*a18*a20 *a8 *b37*u + ----*f(v,v )*f(v,v)*a20 *a8*b37
9 3x 9 2x
10 4 2 20 2 5
+ ----*f(v,v )*a18*a20 *a8*b37*u + ----*f(v,v ) *a20 *a8*b37
9 2x 9 x
20 6 20 5 3 2
+ ----*f(v,v )*f(v,v)*a20 *b37*u + ----*f(v,v )*a18*a20 *b37*u )/(a18
9 x 9 x
4
*a8 )
10 2 3 25 2 3
df(v,s)=(----*u *a18 *a20*a8 *b37*v + ----*u *v *a18 *a20*a8 *b37
9 4x 9 3x x
20 2 2 2 50 2 2 2
- ----*u *a18 *a20 *a8 *b37*u*v - ----*u *u *a18 *a20 *a8 *b37*v
9 3x 9 2x x
10 2 3 50 2 2 2
+ ----*u *v *a18 *a20*a8 *b37 - ----*u *v *a18 *a20 *a8 *b37*u
3 2x 2x 9 2x x
10 4 10 2 3 2
- ----*u *f(v,v)*a18*a20 *a8*b37*v - ----*u *a18 *a20 *a8*b37*u *v
9 2x 9 2x
2 2 2 2 20 2 2 3
- 5*u *v *a18 *a20 *a8 *b37 - ----*u *a18 *a20 *a8*b37*u*v
x x 9 x
5 2 3 20 2 2 2
+ ---*u *v *a18 *a20*a8 *b37 - ----*u *v *a18 *a20 *a8 *b37*u
3 x 3x 3 x 2x
25 4 10 2 3 2
- ----*u *v *f(v,v)*a18*a20 *a8*b37 - ----*u *v *a18 *a20 *a8*b37*u
9 x x 9 x x
5 4 20 5
- ---*u *f(v,v )*a18*a20 *a8*b37*v + ----*u *f(v,v)*a18*a20 *b37*u*v
9 x x 9 x
20 2 4 3 2 4
+ ----*u *a18 *a20 *b37*u *v + v *a18 *a8 *b37
9 x 5x
5 3 2 5 2 2 2 2
- ---*v *f(v,v)*a18*a20 *a8 *b37 - ---*v *a18 *a20 *a8 *b37*u
3 3x 3 3x
5 3 2 5 3 2
- ---*v *f(v,v )*a18*a20 *a8 *b37 - ---*v *f(v ,v )*a18*a20 *a8 *b37
3 2x x 9 x x x
20 3 2 5 2 6
- ----*v *f(v,v )*a18*a20 *a8 *b37 + ---*v *f(v,v) *a20 *b37
9 x 2x 9 x
25 5 2 5 2 4 4
+ ----*v *f(v,v)*a18*a20 *b37*u + ---*v *a18 *a20 *b37*u
9 x 9 x
5 3 2 10 3 2
+ ---*f(v ,v )*a18*a20 *a8 *b37*v + ----*f(v,v )*a18*a20 *a8 *b37*v
3 x 2x 9 3x
10 6 5 5 2
- ----*f(v,v )*f(v,v)*a20 *b37*v + ---*f(v,v )*a18*a20 *b37*u *v)/(
9 x 9 x
2 4
a18 *a8 )
df(u,t)=df(u,x)*f(v,v)*a20 + f(df(v,x),df(v,x))*a8 + f(v,df(v,x,2))*a8 + 2*f(v,
df(v,x))*a20*u$
df(v,t)=( - df(u,x,2)*a18*a20*a8*v - df(u,x)*df(v,x)*a18*a20*a8 + 2*df(u,x)*a18*
a20**2*u*v - df(v,x,3)*a18*a8**2 + df(v,x)*f(v,v)*a20**3 + df(v,x)*a18*a20**2*u
**2 - f(v,df(v,x))*a20**3*v)/a20**2$
df(u,s)=( - 1/9*df(u,x,5)*a18**2*a8**4*b37 + 5/9*df(u,x,3)*df(u,x)*a18**2*a20*a8
**3*b37 - 5/9*df(u,x,3)*f(v,v)*a18*a20**3*a8**2*b37 + 5/9*df(u,x,3)*a18**2*a20**
2*a8**2*b37*u**2 + 5/9*df(u,x,2)**2*a18**2*a20*a8**3*b37 + 20/9*df(u,x,2)*df(u,x
)*a18**2*a20**2*a8**2*b37*u - 20/9*df(u,x,2)*f(v,df(v,x))*a18*a20**3*a8**2*b37 +
5/9*df(u,x)**3*a18**2*a20**2*a8**2*b37 - 5/3*df(u,x)*f(df(v,x),df(v,x))*a18*a20
**3*a8**2*b37 - 10/3*df(u,x)*f(v,df(v,x,2))*a18*a20**3*a8**2*b37 + 20/9*df(u,x)*
f(v,df(v,x))*a18*a20**4*a8*b37*u + 5/9*df(u,x)*f(v,v)**2*a20**6*b37 + 10/3*df(u,
x)*f(v,v)*a18*a20**5*b37*u**2 - 5/9*df(u,x)*a18**2*a20**4*b37*u**4 - 5/3*f(df(v,
x,2),df(v,x,2))*a18*a20**2*a8**3*b37 - 25/9*f(df(v,x),df(v,x,3))*a18*a20**2*a8**
3*b37 - 10/3*f(df(v,x),df(v,x,2))*a18*a20**3*a8**2*b37*u + 10/9*f(df(v,x),df(v,x
))*f(v,v)*a20**5*a8*b37 + 10/9*f(df(v,x),df(v,x))*a18*a20**4*a8*b37*u**2 - 10/9*
f(v,df(v,x,4))*a18*a20**2*a8**3*b37 - 20/9*f(v,df(v,x,3))*a18*a20**3*a8**2*b37*u
+ 10/9*f(v,df(v,x,2))*f(v,v)*a20**5*a8*b37 + 10/9*f(v,df(v,x,2))*a18*a20**4*a8*
b37*u**2 + 20/9*f(v,df(v,x))**2*a20**5*a8*b37 + 20/9*f(v,df(v,x))*f(v,v)*a20**6*
b37*u + 20/9*f(v,df(v,x))*a18*a20**5*b37*u**3)/(a18**2*a8**4)$
df(v,s)=(10/9*df(u,x,4)*a18**2*a20*a8**3*b37*v + 25/9*df(u,x,3)*df(v,x)*a18**2*
a20*a8**3*b37 - 20/9*df(u,x,3)*a18**2*a20**2*a8**2*b37*u*v - 50/9*df(u,x,2)*df(u
,x)*a18**2*a20**2*a8**2*b37*v + 10/3*df(u,x,2)*df(v,x,2)*a18**2*a20*a8**3*b37 -
50/9*df(u,x,2)*df(v,x)*a18**2*a20**2*a8**2*b37*u - 10/9*df(u,x,2)*f(v,v)*a18*a20
**4*a8*b37*v - 10/9*df(u,x,2)*a18**2*a20**3*a8*b37*u**2*v - 5*df(u,x)**2*df(v,x)
*a18**2*a20**2*a8**2*b37 - 20/9*df(u,x)**2*a18**2*a20**3*a8*b37*u*v + 5/3*df(u,x
)*df(v,x,3)*a18**2*a20*a8**3*b37 - 20/3*df(u,x)*df(v,x,2)*a18**2*a20**2*a8**2*
b37*u - 25/9*df(u,x)*df(v,x)*f(v,v)*a18*a20**4*a8*b37 - 10/9*df(u,x)*df(v,x)*a18
**2*a20**3*a8*b37*u**2 - 5/9*df(u,x)*f(v,df(v,x))*a18*a20**4*a8*b37*v + 20/9*df(
u,x)*f(v,v)*a18*a20**5*b37*u*v + 20/9*df(u,x)*a18**2*a20**4*b37*u**3*v + df(v,x,
5)*a18**2*a8**4*b37 - 5/3*df(v,x,3)*f(v,v)*a18*a20**3*a8**2*b37 - 5/3*df(v,x,3)*
a18**2*a20**2*a8**2*b37*u**2 - 5/3*df(v,x,2)*f(v,df(v,x))*a18*a20**3*a8**2*b37 -
5/9*df(v,x)*f(df(v,x),df(v,x))*a18*a20**3*a8**2*b37 - 20/9*df(v,x)*f(v,df(v,x,2
))*a18*a20**3*a8**2*b37 + 5/9*df(v,x)*f(v,v)**2*a20**6*b37 + 25/9*df(v,x)*f(v,v)
*a18*a20**5*b37*u**2 + 5/9*df(v,x)*a18**2*a20**4*b37*u**4 + 5/3*f(df(v,x),df(v,x
,2))*a18*a20**3*a8**2*b37*v + 10/9*f(v,df(v,x,3))*a18*a20**3*a8**2*b37*v - 10/9*
f(v,df(v,x))*f(v,v)*a20**6*b37*v + 5/9*f(v,df(v,x))*a18*a20**5*b37*u**2*v)/(a18
**2*a8**4)$