Solution 6 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
5 2
---*a11 *b23
3
b40=--------------
2
a8
5 2
---*a11 *b23
6
b39=--------------
2
a8
10
----*a11*a9*b23
3
b38=-----------------
2
a8
10
----*a11*a9*b23
3
b37=-----------------
2
a8
5
---*a11*a9*b23
3
b36=----------------
2
a8
5
---*a11*b23
4
b35=-------------
a8
15
----*a11*b23
4
b34=--------------
a8
25
----*a11*b23
6
b33=--------------
a8
25
----*a11*b23
6
b32=--------------
a8
5*a11*b23
b31=-----------
a8
5
---*a11*b23
3
b30=-------------
a8
10 2
----*a9 *b23
3
b29=--------------
2
a8
10 2
----*a9 *b23
3
b28=--------------
2
a8
10
----*a9*b23
3
b27=-------------
a8
5*a9*b23
b26=----------
a8
25
----*a9*b23
6
b25=-------------
a8
5
---*a9*b23
4
b24=------------
a8
5 3
- ---*a11 *b23
3
b22=-----------------
2
a8 *a9
10 2
- ----*a11 *b23
3
b21=------------------
2
a8
5 2
- ---*a11 *b23
6
b20=-----------------
2
a8
15 2
- ----*a11 *b23
2
b19=------------------
a8*a9
5 2
- ---*a11 *b23
2
b18=-----------------
a8*a9
5 2
- ---*a11 *b23
2
b17=-----------------
a8*a9
5 2
- ---*a11 *b23
2
b16=-----------------
a8*a9
b15=0
b14=0
5
- ---*a11*b23
2
b13=----------------
a8
5
---*a11*b23
2
b12=-------------
a8
10
- ----*a11*b23
3
b11=-----------------
a8
5
---*a11*b23
3
b10=-------------
a8
5
- ---*a11*b23
2
b9=----------------
a8
5
- ---*a11*b23
6
b8=----------------
a8
15
- ----*a11*b23
16
b7=-----------------
a9
5
----*a11*b23
16
b6=--------------
a9
5
---*a11*b23
8
b5=-------------
a9
10 2
----*a9 *b23
3
b4=--------------
2
a8
5
---*a9*b23
3
b3=------------
a8
5
---*a9*b23
6
b2=------------
a8
1
b1=----*b23
16
a12=a11
a10=2*a9
2
- a11
a7=---------
a9
a6=0
a5=0
3
- ---*a11*a8
4
a4=---------------
a9
3
---*a11*a8
4
a3=------------
a9
a2=2*a9
1
a1=---*a8
4
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:
b23,a11,a9,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
1 2 3 3
df(u,t)=(---*u *a8*a9 + 2*u *a9 *u + ---*f(v ,v )*a11*a8 - ---*f(v,v )*a11*a8
4 3x x 4 x 2x 4 3x
2
- f(v,v )*f(v,v)*a11 )/a9
x
df(v,t)=u *a9*v + v *a8 + v *f(v,v)*a11 + 2*v *a9*u + f(v,v )*a11*v
x 3x x x x
1 2 5
df(u,s)=(----*u *a8 *a9*b23 - ---*u *f(v,v)*a11*a8*a9*b23
16 5x 6 3x
5 2 5 2
+ ---*u *a8*a9 *b23*u + ---*u *u *a8*a9 *b23
6 3x 3 2x x
5 5
- ---*u *f(v,v )*a11*a8*a9*b23 + ---*u *f(v ,v )*a11*a8*a9*b23
2 2x x 3 x x x
10 5 2 2
- ----*u *f(v,v )*a11*a8*a9*b23 - ---*u *f(v,v) *a11 *a9*b23
3 x 2x 6 x
10 3 2 5 2
+ ----*u *a9 *b23*u + ---*f(v ,v )*a11*a8 *b23
3 x 8 2x 3x
5 2 5 2
+ ----*f(v ,v )*a11*a8 *b23 - ---*f(v ,v )*f(v,v)*a11 *a8*b23
16 x 4x 2 x 2x
5 5 2
+ ---*f(v ,v )*a11*a8*a9*b23*u - ---*f(v ,v )*f(v,v )*a11 *a8*b23
2 x 2x 2 x x x
15 2 5 2
- ----*f(v,v )*a11*a8 *b23 - ---*f(v,v )*f(v,v)*a11 *a8*b23
16 5x 2 3x
5 15 2
- ---*f(v,v )*a11*a8*a9*b23*u - ----*f(v,v )*f(v,v )*a11 *a8*b23
2 3x 2 2x x
5 2 3 10 2
- ---*f(v,v )*f(v,v) *a11 *b23 - ----*f(v,v )*f(v,v)*a11 *a9*b23*u)/(
3 x 3 x
2
a8 *a9)
5 25
df(v,s)=(---*u *a8*a9*b23*v + ----*u *v *a8*a9*b23 + 5*u *v *a8*a9*b23
4 3x 6 2x x x 2x
5 10 2 2
+ ---*u *f(v,v)*a11*a9*b23*v + ----*u *a9 *b23*u*v + v *a8 *b23
3 x 3 x 5x
5 10
+ ---*v *f(v,v)*a11*a8*b23 + ----*v *a8*a9*b23*u
3 3x 3 3x
25
+ 5*v *f(v,v )*a11*a8*b23 + ----*v *f(v ,v )*a11*a8*b23
2x x 6 x x x
25 5 2 2
+ ----*v *f(v,v )*a11*a8*b23 + ---*v *f(v,v) *a11 *b23
6 x 2x 6 x
10 10 2 2
+ ----*v *f(v,v)*a11*a9*b23*u + ----*v *a9 *b23*u
3 x 3 x
15 5
+ ----*f(v ,v )*a11*a8*b23*v + ---*f(v,v )*a11*a8*b23*v
4 x 2x 4 3x
5 2 10 2
+ ---*f(v,v )*f(v,v)*a11 *b23*v + ----*f(v,v )*a11*a9*b23*u*v)/a8
3 x 3 x