Solution 15 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
a11*a3*a9*b1
b40=--------------
3
a1
3 2
---*a11 *b1
2
b39=-------------
2
a1
6*a11*a9*b1
b38=-------------
2
a1
2
18*a11 *b1
b37=------------
a1*a3
3*a11*a9*b1
b36=-------------
2
a1
1
---*a3*a9*b1
3
b35=--------------
2
a1
a3*a9*b1
b34=----------
2
a1
2*a11*b1
b33=----------
a1
2*a11*b1
b32=----------
a1
b31=0
b30=0
2
54*a11 *b1
b29=------------
2
a3
18*a11*a9*b1
b28=--------------
a1*a3
b27=0
b26=0
6*a11*b1
b25=----------
a3
a9*b1
b24=-------
a1
b23=0
2 1 2
2*a1*a11 *a3*b1 - ---*a11*a3 *a9*b1
3
b22=-------------------------------------
4
a1
2
24*a1*a11 *b1 - 2*a11*a3*a9*b1
b21=--------------------------------
3
a1
15 2
----*a1*a11 *b1 - a11*a3*a9*b1
2
b20=--------------------------------
3
a1
6*a11*a3*b1
b19=-------------
2
a1
5 1 2
---*a1*a11*a3*b1 - ---*a3 *a9*b1
3 9
b18=----------------------------------
3
a1
6*a11*a3*b1
b17=-------------
2
a1
1 2
5*a1*a11*a3*b1 - ---*a3 *a9*b1
3
b16=--------------------------------
3
a1
2
72*a11 *b1
b15=------------
a1*a3
2
90*a1*a11 *b1 - 6*a11*a3*a9*b1
b14=--------------------------------
2
a1 *a3
10*a11*b1
b13=-----------
a1
30*a11*b1
b12=-----------
a1
20*a11*b1
b11=-----------
a1
20*a11*b1
b10=-----------
a1
18*a11*b1
b9=-----------
a1
1
5*a1*a11*b1 - ---*a3*a9*b1
3
b8=----------------------------
2
a1
1
---*a3*b1
3
b7=-----------
a1
5
---*a3*b1
3
b6=-----------
a1
10
----*a3*b1
3
b5=------------
a1
2
270*a11 *b1
b4=-------------
2
a3
60*a11*b1
b3=-----------
a3
30*a11*b1
b2=-----------
a3
1
---*a3*a9
3
a12=-----------
a1
6*a1*a11
a10=----------
a3
a8=0
2 1 2
---*a1*a11*a3 - ---*a3 *a9
3 9
a7=----------------------------
2
a1
a6=4*a11
1
3*a1*a11 - ---*a3*a9
3
a5=----------------------
a1
1
a4=---*a3
3
18*a1*a11
a2=-----------
a3
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:
b1,a11,a3,a9,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 1 2
df(u,t)=(u *a1 *a3 + 3*u *f(v,v)*a1 *a11*a3 - ---*u *f(v,v)*a1*a3 *a9
3x x 3 x
3 2 2 1 2 2
+ 18*u *a1 *a11*u + f(v ,v )*a1 *a3 + ---*f(v,v )*a1 *a3
x x 2x 3 3x
2 2 1 3
+ ---*f(v,v )*f(v,v)*a1*a11*a3 - ---*f(v,v )*f(v,v)*a3 *a9
3 x 9 x
2 2
+ 4*f(v,v )*a1 *a11*a3*u)/(a1 *a3)
x
df(v,t)=
2 1 2
u *a1*a3*a9*v + v *f(v,v)*a1*a11*a3 + 6*v *a1 *a11*u + ---*f(v,v )*a3 *a9*v
x x x 3 x
-----------------------------------------------------------------------------
a1*a3
4 2 3 2
df(u,s)=(u *a1 *a3 *b1 + 5*u *f(v,v)*a1 *a11*a3 *b1
5x 3x
1 2 3 4
- ---*u *f(v,v)*a1 *a3 *a9*b1 + 30*u *a1 *a11*a3*b1*u
3 3x 3x
4 3 2
+ 60*u *u *a1 *a11*a3*b1 + 18*u *f(v,v )*a1 *a11*a3 *b1
2x x 2x x
3 2 3 2
+ 20*u *f(v ,v )*a1 *a11*a3 *b1 + 20*u *f(v,v )*a1 *a11*a3 *b1
x x x x 2x
15 2 2 2 2 2 3
+ ----*u *f(v,v) *a1 *a11 *a3 *b1 - u *f(v,v) *a1*a11*a3 *a9*b1
2 x x
3 2 2 2
+ 90*u *f(v,v)*a1 *a11 *a3*b1*u - 6*u *f(v,v)*a1 *a11*a3 *a9*b1*u
x x
4 2 2 10 3 3
+ 270*u *a1 *a11 *b1*u + ----*f(v ,v )*a1 *a3 *b1
x 3 2x 3x
5 3 3 2 3
+ ---*f(v ,v )*a1 *a3 *b1 + 5*f(v ,v )*f(v,v)*a1 *a11*a3 *b1
3 x 4x x 2x
1 4 3 2
- ---*f(v ,v )*f(v,v)*a1*a3 *a9*b1 + 30*f(v ,v )*a1 *a11*a3 *b1*u
3 x 2x x 2x
2 3 1 3 3
+ 6*f(v ,v )*f(v,v )*a1 *a11*a3 *b1 + ---*f(v,v )*a1 *a3 *b1
x x x 3 5x
5 2 3
+ ---*f(v,v )*f(v,v)*a1 *a11*a3 *b1
3 3x
1 4 3 2
- ---*f(v,v )*f(v,v)*a1*a3 *a9*b1 + 10*f(v,v )*a1 *a11*a3 *b1*u
9 3x 3x
2 3 2 2 3
+ 6*f(v,v )*f(v,v )*a1 *a11*a3 *b1 + 2*f(v,v )*f(v,v) *a1*a11 *a3 *b1
2x x x
1 2 4
- ---*f(v,v )*f(v,v) *a11*a3 *a9*b1
3 x
2 2 2
+ 24*f(v,v )*f(v,v)*a1 *a11 *a3 *b1*u
x
3 3 2 2
- 2*f(v,v )*f(v,v)*a1*a11*a3 *a9*b1*u + 72*f(v,v )*a1 *a11 *a3*b1*u )/
x x
4 2
(a1 *a3 )
2 2 3
df(v,s)=(u *a1 *a3 *a9*b1*v + 6*u *v *a1 *a11*a3*b1
3x 2x x
2 2
+ 3*u *f(v,v)*a1*a11*a3 *a9*b1*v + 18*u *a1 *a11*a3*a9*b1*u*v
x x
2 2 2 2
+ 2*v *f(v ,v )*a1 *a11*a3 *b1 + 2*v *f(v,v )*a1 *a11*a3 *b1
x x x x 2x
3 2 2 2 2 2
+ ---*v *f(v,v) *a1*a11 *a3 *b1 + 18*v *f(v,v)*a1 *a11 *a3*b1*u
2 x x
3 2 2 3
+ 54*v *a1 *a11 *b1*u + f(v ,v )*a1*a3 *a9*b1*v
x x 2x
1 3 3
+ ---*f(v,v )*a1*a3 *a9*b1*v + f(v,v )*f(v,v)*a11*a3 *a9*b1*v
3 3x x
2 3 2
+ 6*f(v,v )*a1*a11*a3 *a9*b1*u*v)/(a1 *a3 )
x