Solution 1 to problem l1o13
Expressions |
Parameters |
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Back to problem l1o13
Expressions
The solution is given through the following expressions:
2
2*a3*a5 *b1
b21=-------------
3
a0
2*a3*a5*b1
b20=------------
2
a0
b19=0
3
- 2*a5 *b1
b18=-------------
3
a0
b17=0
b16=0
b15=0
b14=0
a5*b1
b13=-------
a0
b12=0
2
2*a3 *a5*b1
b11=-------------
3
a0
2
- 2*a3*a5 *b1
b10=----------------
3
a0
4*a3*a5*b1
b9=------------
2
a0
4*a3*a5*b1
b8=------------
2
a0
2*a3*b1
b7=---------
a0
2*a3*b1
b6=---------
a0
b5=0
2
- 6*a5 *b1
b4=-------------
2
a0
b3=0
b2=0
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, a3, a5, a0, a4
Relevance for the application:
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df(u,t)=u *a0 + u *a4 + f(v,v)*a3
x x
df(v,t)=v *a4 + a5*u*v
x
3 2 2
df(u,s)=(u *a0 *b1 + 4*u *f(v,v)*a0*a3*a5*b1 - 6*u *a0*a5 *b1*u
3x x x
2 2
+ 2*f(v ,v )*a0 *a3*b1 + 2*f(v,v )*a0 *a3*b1
x x 2x
2 2
+ 4*f(v,v )*a0*a3*a5*b1*u + 2*f(v,v) *a3 *a5*b1
x
2 2 3
- 2*f(v,v)*a3*a5 *b1*u )/a0
2 2
df(v,s)=(u *a0 *a5*b1*v + 2*f(v,v )*a0*a3*a5*b1*v + 2*f(v,v)*a3*a5 *b1*u*v
2x x
3 3 3
- 2*a5 *b1*u *v)/a0