Solution 2 to problem l1o23
Expressions |
Parameters |
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Back to problem l1o23
Expressions
The solution is given through the following expressions:
2
- 4*a10 *b1
b21=--------------
a1*a4
2*a10*b1
b20=----------
a1
b19=0
3
32*a10 *b1
b18=------------
3
a4
b17=0
2
- 24*a10 *b1
b16=---------------
2
a4
b15=0
b14=0
2*a10*b1
b13=----------
a4
b12=0
b11=0
b10=0
- 4*a10*b1
b9=-------------
a1
- 2*a10*b1
b8=-------------
a1
a4*b1
b7=-------
a1
a4*b1
b6=-------
a1
b5=0
2
48*a10 *b1
b4=------------
2
a4
- 12*a10*b1
b3=--------------
a4
- 12*a10*b1
b2=--------------
a4
2
- 8*a10 *a1
a9=--------------
2
a4
a8=0
2*a10*a1
a7=----------
a4
a6=0
a5=0
a3=0
- 8*a10*a1
a2=-------------
a4
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,a10,a4,a1
Relevance for the application:
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2
u *a1*a4 - 8*u *a10*a1*u + f(v,v )*a4
2x x x
df(u,t)=-----------------------------------------
a4
2 2 2
2*u *a10*a1*a4*v + f(v,v)*a10*a4 *v - 8*a10 *a1*u *v
x
df(v,t)=------------------------------------------------------
2
a4
2 2
df(u,s)=(u *a1*a4 *b1 - 12*u *a10*a1*a4*b1*u - 12*u *a10*a1*a4*b1
3x 2x x
2 2 2 3
- 2*u *f(v,v)*a10*a4 *b1 + 48*u *a10 *a1*b1*u + f(v ,v )*a4 *b1
x x x x
3 2 2
+ f(v,v )*a4 *b1 - 4*f(v,v )*a10*a4 *b1*u)/(a1*a4 )
2x x
2 2
df(v,s)=(2*u *a10*a1*a4 *b1*v - 24*u *a10 *a1*a4*b1*u*v
2x x
3 2 2
+ 2*f(v,v )*a10*a4 *b1*v - 4*f(v,v)*a10 *a4 *b1*u*v
x
3 3 3
+ 32*a10 *a1*b1*u *v)/(a1*a4 )