Solution 2 to problem l1o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=0
b72=0
b71=0
b70=0
b69=(4/2025*a3**3*a7*b37)/a13**4
b68=( - 2/135*a3**2*a7*b37)/a13**3
b67=(2/135*a3**2*a7*b37)/a13**3
b66=0
b65=0
b64=( - 2/135*a3**2*a7*b37)/a13**3
b63=0
b62=( - 1/135*a3**2*a7*b37)/a13**3
b61=(1/18*a3*a7*b37)/a13**2
b60=( - 1/18*a3*a7*b37)/a13**2
b59=0
b58=0
b57=0
b56=0
b55=0
b54=(16/10125*a3**4*b37)/a13**4
b53=(16/10125*a3**4*b37)/a13**4
b52=( - 16/675*a3**3*b37)/a13**3
b51=( - 16/225*a3**3*b37)/a13**3
b50=( - 2/75*a3**3*b37)/a13**3
b49=( - 4/225*a3**3*b37)/a13**3
b48=(8/45*a3**2*b37)/a13**2
b47=(8/15*a3**2*b37)/a13**2
b46=(4/15*a3**2*b37)/a13**2
b45=(16/45*a3**2*b37)/a13**2
b44=(7/45*a3**2*b37)/a13**2
b43=(7/90*a3**2*b37)/a13**2
b42=( - 2/3*a3*b37)/a13
b41=( - 4/3*a3*b37)/a13
b40=( - 4/3*a3*b37)/a13
b39=( - 2/3*a3*b37)/a13
b38=( - 1/8*a3*b37)/a13
b36=0
b35=0
b34=0
b33=0
b32=0
b31=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=(4/135*a3**2*a7*b37)/a13**3
b23=(2/135*a3**2*a7*b37)/a13**3
b22=(2/135*a3**2*a7*b37)/a13**3
b21=( - 1/9*a3*a7*b37)/a13**2
b20=(1/9*a3*a7*b37)/a13**2
b19=( - 2/9*a3*a7*b37)/a13**2
b18=0
b17=( - 2/9*a3*a7*b37)/a13**2
b16=( - 1/18*a3*a7*b37)/a13**2
b15=(5/12*a7*b37)/a13
b14=0
b13=( - 5/12*a7*b37)/a13
b12=0
b11=(16/10125*a3**4*b37)/a13**4
b10=( - 8/225*a3**3*b37)/a13**3
b9=( - 8/675*a3**3*b37)/a13**3
b8=(1/15*a3**2*b37)/a13**2
b7=(2/9*a3**2*b37)/a13**2
b6=(2/45*a3**2*b37)/a13**2
b5=( - 1/6*a3*b37)/a13
b4=( - 1/4*a3*b37)/a13
b3=( - 1/12*a3*b37)/a13
b2=1/16*b37
a22=( - 4/225*a3**2*a7)/a13**2
a21=(2/15*a3*a7)/a13
a20=0
a19=( - 16/1125*a3**3)/a13**2
a18=(4/75*a3**2)/a13
a17=(14/75*a3**2)/a13
a16= - 2/5*a3
a15= - 2/5*a3
a14= - 3/10*a3
a12=0
a11=0
a10=( - 4/15*a3*a7)/a13
a9=( - 2/15*a3*a7)/a13
a8=a7
a6=0
a5=( - 4/15*a3**2)/a13
a4=a3
a2= - 5/4*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,a7,a3,a13
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
5 2 2 2
df(u,t)=( - ---*u *a13 + u *a13*a3*u + u *a13*a3 - ----*u *f(v,v)*a3*a7
4 3x 2x x 15 x
4 2 2
- ----*u *a3 *u + f(v ,v )*a13*a7 + f(v,v )*a13*a7
15 x x x 2x
4
- ----*f(v,v )*a3*a7*u)/a13
15 x
3 2 2 2 14 2
df(v,t)=( - ----*u *a13 *a3*v - ---*u *v *a13 *a3 + ----*u *a13*a3 *u*v
10 2x 5 x x 75 x
3 2 2 4 2 2
+ v *a13 - ---*v *a13 *a3*u + ----*v *a13*a3 *u
3x 5 2x 75 x
2 4 2 16 3 3
+ ----*f(v,v )*a13*a3*a7*v - -----*f(v,v)*a3 *a7*u*v - ------*a3 *u *v
15 x 225 1125
2
)/a13
1 4 1 3 1 3
df(u,s)=(----*u *a13 *b37 - ----*u *a13 *a3*b37*u - ---*u *u *a13 *a3*b37
16 5x 12 4x 4 3x x
1 2 2 2 2 2
- ----*u *f(v,v)*a13 *a3*a7*b37 + ----*u *a13 *a3 *b37*u
18 3x 45 3x
1 2 3 2 2 2
- ---*u *a13 *a3*b37 + ---*u *u *a13 *a3 *b37*u
6 2x 9 2x x
2 2 2 2
- ---*u *f(v,v )*a13 *a3*a7*b37 + -----*u *f(v,v)*a13*a3 *a7*b37*u
9 2x x 135 2x
8 3 3 1 3 2 2
- -----*u *a13*a3 *b37*u + ----*u *a13 *a3 *b37
675 2x 15 x
2 2 2 8 2 3 2
+ -----*u *f(v,v)*a13*a3 *a7*b37 - -----*u *a13*a3 *b37*u
135 x 225 x
2 2 4 2
- ---*u *f(v,v )*a13 *a3*a7*b37 + -----*u *f(v,v )*a13*a3 *a7*b37*u
9 x 2x 135 x x
16 4 4 5 3
+ -------*u *a3 *b37*u - ----*f(v ,v )*a13 *a7*b37
10125 x 12 2x 2x
1 2 5 3
+ ---*f(v ,v )*a13 *a3*a7*b37*u + ----*f(v,v )*a13 *a7*b37
9 x 2x 12 4x
1 2 4
- ---*f(v,v )*a13 *a3*a7*b37*u)/a13
9 3x
1 3 2 3
df(v,s)=( - ---*u *a13 *a3*b37*v - ---*u *v *a13 *a3*b37
8 4x 3 3x x
7 2 2 7 2 2
+ ----*u *a13 *a3 *b37*u*v + ----*u *u *a13 *a3 *b37*v
90 3x 45 2x x
4 3 16 2 2
- ---*u *v *a13 *a3*b37 + ----*u *v *a13 *a3 *b37*u
3 2x 2x 45 2x x
1 2 4 3 2
- -----*u *f(v,v)*a13*a3 *a7*b37*v - -----*u *a13*a3 *b37*u *v
135 2x 225 2x
4 2 2 2 2 2 3
+ ----*u *v *a13 *a3 *b37 - ----*u *a13*a3 *b37*u*v
15 x x 75 x
4 3 8 2 2
- ---*u *v *a13 *a3*b37 + ----*u *v *a13 *a3 *b37*u
3 x 3x 15 x 2x
16 3 2 2 2
- -----*u *v *a13*a3 *b37*u - -----*u *f(v,v )*a13*a3 *a7*b37*v
225 x x 135 x x
4 3 16 4 3
+ ------*u *f(v,v)*a3 *a7*b37*u*v + -------*u *a3 *b37*u *v
2025 x 10125 x
4 2 3 8 2 2 2
+ v *a13 *b37 - ---*v *a13 *a3*b37*u + ----*v *a13 *a3 *b37*u
5x 3 4x 45 3x
16 3 3 16 4 4
- -----*v *a13*a3 *b37*u + -------*v *a3 *b37*u
675 2x 10125 x
1 2 2 2
- ----*f(v ,v )*a13 *a3*a7*b37*v + -----*f(v ,v )*a13*a3 *a7*b37*u*v
18 x 2x 135 x x
1 2 2 2
+ ----*f(v,v )*a13 *a3*a7*b37*v - -----*f(v,v )*a13*a3 *a7*b37*u*v)/
18 3x 135 2x
4
a13
df(u,t)=( - 5/4*df(u,x,3)*a13**2 + df(u,x,2)*a13*a3*u + df(u,x)**2*a13*a3 - 2/15
*df(u,x)*f(v,v)*a3*a7 - 4/15*df(u,x)*a3**2*u**2 + f(df(v,x),df(v,x))*a13*a7 + f(
v,df(v,x,2))*a13*a7 - 4/15*f(v,df(v,x))*a3*a7*u)/a13$
df(v,t)=( - 3/10*df(u,x,2)*a13**2*a3*v - 2/5*df(u,x)*df(v,x)*a13**2*a3 + 14/75*
df(u,x)*a13*a3**2*u*v + df(v,x,3)*a13**3 - 2/5*df(v,x,2)*a13**2*a3*u + 4/75*df(v
,x)*a13*a3**2*u**2 + 2/15*f(v,df(v,x))*a13*a3*a7*v - 4/225*f(v,v)*a3**2*a7*u*v -
16/1125*a3**3*u**3*v)/a13**2$
df(u,s)=(1/16*df(u,x,5)*a13**4*b37 - 1/12*df(u,x,4)*a13**3*a3*b37*u - 1/4*df(u,x
,3)*df(u,x)*a13**3*a3*b37 - 1/18*df(u,x,3)*f(v,v)*a13**2*a3*a7*b37 + 2/45*df(u,x
,3)*a13**2*a3**2*b37*u**2 - 1/6*df(u,x,2)**2*a13**3*a3*b37 + 2/9*df(u,x,2)*df(u,
x)*a13**2*a3**2*b37*u - 2/9*df(u,x,2)*f(v,df(v,x))*a13**2*a3*a7*b37 + 2/135*df(u
,x,2)*f(v,v)*a13*a3**2*a7*b37*u - 8/675*df(u,x,2)*a13*a3**3*b37*u**3 + 1/15*df(u
,x)**3*a13**2*a3**2*b37 + 2/135*df(u,x)**2*f(v,v)*a13*a3**2*a7*b37 - 8/225*df(u,
x)**2*a13*a3**3*b37*u**2 - 2/9*df(u,x)*f(v,df(v,x,2))*a13**2*a3*a7*b37 + 4/135*
df(u,x)*f(v,df(v,x))*a13*a3**2*a7*b37*u + 16/10125*df(u,x)*a3**4*b37*u**4 - 5/12
*f(df(v,x,2),df(v,x,2))*a13**3*a7*b37 + 1/9*f(df(v,x),df(v,x,2))*a13**2*a3*a7*
b37*u + 5/12*f(v,df(v,x,4))*a13**3*a7*b37 - 1/9*f(v,df(v,x,3))*a13**2*a3*a7*b37*
u)/a13**4$
df(v,s)=( - 1/8*df(u,x,4)*a13**3*a3*b37*v - 2/3*df(u,x,3)*df(v,x)*a13**3*a3*b37
+ 7/90*df(u,x,3)*a13**2*a3**2*b37*u*v + 7/45*df(u,x,2)*df(u,x)*a13**2*a3**2*b37*
v - 4/3*df(u,x,2)*df(v,x,2)*a13**3*a3*b37 + 16/45*df(u,x,2)*df(v,x)*a13**2*a3**2
*b37*u - 1/135*df(u,x,2)*f(v,v)*a13*a3**2*a7*b37*v - 4/225*df(u,x,2)*a13*a3**3*
b37*u**2*v + 4/15*df(u,x)**2*df(v,x)*a13**2*a3**2*b37 - 2/75*df(u,x)**2*a13*a3**
3*b37*u*v - 4/3*df(u,x)*df(v,x,3)*a13**3*a3*b37 + 8/15*df(u,x)*df(v,x,2)*a13**2*
a3**2*b37*u - 16/225*df(u,x)*df(v,x)*a13*a3**3*b37*u**2 - 2/135*df(u,x)*f(v,df(v
,x))*a13*a3**2*a7*b37*v + 4/2025*df(u,x)*f(v,v)*a3**3*a7*b37*u*v + 16/10125*df(u
,x)*a3**4*b37*u**3*v + df(v,x,5)*a13**4*b37 - 2/3*df(v,x,4)*a13**3*a3*b37*u + 8/
45*df(v,x,3)*a13**2*a3**2*b37*u**2 - 16/675*df(v,x,2)*a13*a3**3*b37*u**3 + 16/
10125*df(v,x)*a3**4*b37*u**4 - 1/18*f(df(v,x),df(v,x,2))*a13**2*a3*a7*b37*v + 2/
135*f(df(v,x),df(v,x))*a13*a3**2*a7*b37*u*v + 1/18*f(v,df(v,x,3))*a13**2*a3*a7*
b37*v - 2/135*f(v,df(v,x,2))*a13*a3**2*a7*b37*u*v)/a13**4$