Solution 2 to problem l21o23
Expressions |
Parameters |
Relevance |
Back to problem l21o23
Expressions
The solution is given through the following expressions:
a3*b9
b12=-------
a1
b11=0
b10=0
b8=0
2
- a3 *b9
b7=-----------
2
a1
b6=0
- a3*b9
b5=----------
a1
a3*b9
b4=-------
a8
3*a3*b9
b3=---------
a8
b2=0
a1*b9
b1=-------
a8
1
---*a3*a8
2
a9=-----------
a1
a7=0
1 2
- ---*a3 *a8
2
a6=---------------
2
a1
- a3*a8
a5=----------
a1
a4=a3
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:
b9,a3,a1,a8
Relevance for the application:
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3 2 2 1 2 2
u = (u *a1 + f(v ,v )*a1 *a3 + f(v,v )*a1 *a3 - ---*f(v,v) *a3 *a8
t 2x x x 2x 2
2
- f(v,v)*a1*a3*a8*u)/a1
1
---*f(v,v)*a3*a8*v + a1*a8*u*v
2
v = --------------------------------
t a1
3 2
u = (u *a1 *b9 - u *f(v,v)*a1*a3*a8*b9 + 3*f(v ,v )*a1 *a3*b9
s 3x x x 2x
2 2 2
+ f(v,v )*a1 *a3*b9 - f(v,v )*f(v,v)*a3 *a8*b9)/(a1 *a8)
3x x
u *a1*b9*v + f(v,v )*a3*b9*v
x x
v = ------------------------------
s a1