Solution 7 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
5 2
---*a11 *b23
6
b39=--------------
2
a8
b38=0
5
- ---*a11*a2*b23
3
b37=-------------------
2
a8
5
- ---*a11*a2*b23
9
b36=-------------------
2
a8
b35=0
5
---*a11*b23
3
b34=-------------
a8
10
----*a11*b23
3
b33=--------------
a8
5
---*a11*b23
2
b32=-------------
a8
10
----*a11*b23
3
b31=--------------
a8
5
---*a11*b23
3
b30=-------------
a8
5 2
----*a2 *b23
18
b29=--------------
2
a8
5 2
---*a2 *b23
9
b28=-------------
2
a8
5
- ---*a2*b23
3
b27=---------------
a8
10
- ----*a2*b23
3
b26=----------------
a8
5
- ---*a2*b23
2
b25=---------------
a8
5
- ---*a2*b23
6
b24=---------------
a8
b22=0
b21=0
5 2
- ----*a11 *b23
18
b20=------------------
2
a8
b19=0
b18=0
10 2
- ----*a11 *b23
3
b17=------------------
a2*a8
5 2
- ---*a11 *b23
3
b16=-----------------
a2*a8
b15=0
5
---*a11*a2*b23
9
b14=----------------
2
a8
b13=0
5
---*a11*b23
3
b12=-------------
a8
5
- ---*a11*b23
3
b11=----------------
a8
5
---*a11*b23
6
b10=-------------
a8
5
- ---*a11*b23
3
b9=----------------
a8
5
- ---*a11*b23
6
b8=----------------
a8
b7=0
5
- ---*a11*b23
2
b6=----------------
a2
5
- ---*a11*b23
2
b5=----------------
a2
5 2
- ---*a2 *b23
6
b4=----------------
2
a8
5
---*a2*b23
3
b3=------------
a8
5
---*a2*b23
6
b2=------------
a8
1
b1= - ---*b23
4
a12=0
a10= - a2
a9= - a2
a7=0
a6=0
a5= - a11
a4=0
- 3*a11*a8
a3=-------------
a2
1
a1= - ---*a8
2
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,a2,a11,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
1 2
- ---*u *a2*a8 - u *f(v,v)*a11*a2 + u *a2 *u - 3*f(v ,v )*a11*a8
2 3x x x x 2x
df(u,t)=---------------------------------------------------------------------
a2
df(v,t)= - u *a2*v + v *a8 + v *f(v,v)*a11 - v *a2*u
x 3x x x
1 2 5
df(u,s)=( - ---*u *a2*a8 *b23 - ---*u *f(v,v)*a11*a2*a8*b23
4 5x 6 3x
5 2 5 2
+ ---*u *a2 *a8*b23*u + ---*u *u *a2 *a8*b23
6 3x 3 2x x
5 5
- ---*u *f(v,v )*a11*a2*a8*b23 + ---*u *f(v ,v )*a11*a2*a8*b23
3 2x x 6 x x x
5 5 2 2
- ---*u *f(v,v )*a11*a2*a8*b23 - ----*u *f(v,v) *a11 *a2*b23
3 x 2x 18 x
5 2 5 3 2
+ ---*u *f(v,v)*a11*a2 *b23*u - ---*u *a2 *b23*u
9 x 6 x
5 2 5 2
- ---*f(v ,v )*a11*a8 *b23 - ---*f(v ,v )*a11*a8 *b23
2 2x 3x 2 x 4x
5 2 5
- ---*f(v ,v )*f(v,v)*a11 *a8*b23 + ---*f(v ,v )*a11*a2*a8*b23*u
3 x 2x 3 x 2x
10 2 2
- ----*f(v ,v )*f(v,v )*a11 *a8*b23)/(a2*a8 )
3 x x x
5 5 10
df(v,s)=( - ---*u *a2*a8*b23*v - ---*u *v *a2*a8*b23 - ----*u *v *a2*a8*b23
6 3x 2 2x x 3 x 2x
5 5 2 2
- ---*u *f(v,v)*a11*a2*b23*v + ---*u *a2 *b23*u*v + v *a8 *b23
9 x 9 x 5x
5 5
+ ---*v *f(v,v)*a11*a8*b23 - ---*v *a2*a8*b23*u
3 3x 3 3x
10 5
+ ----*v *f(v,v )*a11*a8*b23 + ---*v *f(v ,v )*a11*a8*b23
3 2x x 2 x x x
10 5 2 2
+ ----*v *f(v,v )*a11*a8*b23 + ---*v *f(v,v) *a11 *b23
3 x 2x 6 x
5 5 2 2
- ---*v *f(v,v)*a11*a2*b23*u + ----*v *a2 *b23*u
3 x 18 x
5 2
+ ---*f(v ,v )*a11*a8*b23*v)/a8
3 x 2x