Solution 4 to problem l112o12
Expressions |
Parameters |
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Back to problem l112o12
Expressions
The solution is given through the following expressions:
1
- ---*a5*b18
2
b19=---------------
a8
b17=0
1
- ---*a5*b14
2
b16=---------------
a8
b15=0
b13=0
b12=0
1 3 1 2
- ---*a5 *b3 - ---*a5 *a8*b18
8 2
b11=--------------------------------
3
a8
3 2
---*a5 *b3 + a5*a8*b18
4
b10=------------------------
2
a8
1 2 1 2
- ---*a5 *b14 + ---*a5 *b2
2 2
b9=-----------------------------
2
a8
3
- ---*a5*b3
2
b8=--------------
a8
a5*b14 - a5*b2
b7=----------------
a8
1
- ---*a5*b2
2
b6=--------------
a8
- a5*b1
b5=----------
a8
- a5*b1
b4=----------
a8
a7=0
a4=0
a3=0
a2=0
a0=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:
b18, b14, b3, b2, b1, a5, a8
Relevance for the application:
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2
df(u,t)=u *a6 + f(v,v) *a5
x
df(v,t)=v *a6 + f(v,v)*a8*v
x
3 1 2 3
df(u,s)=(u *a8 *b1 - ---*u *f(v,v)*a5*a8 *b2 + u *a8 *b2*u
2x 2 x x
2 2
- f(v ,v )*a5*a8 *b1 - f(v,v )*a5*a8 *b1
x x 2x
1 2 1 2
- ---*f(v,v )*f(v,v)*a5 *a8*b14 + ---*f(v,v )*f(v,v)*a5 *a8*b2
2 x 2 x
2 2 1 3 3
+ f(v,v )*a5*a8 *b14*u - f(v,v )*a5*a8 *b2*u - ---*f(v,v) *a5 *b3
x x 8
1 3 2 3 2 2
- ---*f(v,v) *a5 *a8*b18 + ---*f(v,v) *a5 *a8*b3*u
2 4
2 2 3 2 2 3 3 3
+ f(v,v) *a5*a8 *b18*u - ---*f(v,v)*a5*a8 *b3*u + a8 *b3*u )/a8
2
1 1 2
df(v,s)=( - ---*v *f(v,v)*a5*b14 + v *a8*b14*u - ---*f(v,v) *a5*b18*v
2 x x 2
+ f(v,v)*a8*b18*u*v)/a8