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