Solution 1 to problem l2313o24
Expressions |
Parameters |
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Back to problem l2313o24
Expressions
The solution is given through the following expressions:
b66=0
b65=0
b64=0
b63=0
b62=0
a12*a3*b1
b61=-----------
2
a1
a12*a3*b1
b60=-----------
2
a1
b59=0
b58=0
b57=0
b56=0
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
a12*b1
b49=--------
a1
b48=0
b47=0
b46=0
b45=0
b44=0
b43=0
b42=0
b41=0
b40=0
b39=0
b38=0
b37=0
b36=0
b35=0
b34=0
b33=0
b32=0
b31=0
b30=0
b29=0
2
- a12*a3 *b1
b28=---------------
3
a1
2
- a12*a3 *b1
b27=---------------
3
a1
b26=0
b25=0
b24=0
b23=0
b22=0
- a12*a3*b1
b21=--------------
2
a1
b20=0
b19=0
b18=0
b17=0
b16=0
b15=0
b14=0
b13=0
b12=0
b11=0
b10=0
b9=0
b8=0
a3*b1
b7=-------
a1
4*a3*b1
b6=---------
a1
3*a3*b1
b5=---------
a1
b4=0
b3=0
b2=0
1
---*a12*a3
2
a13=------------
a1
a11=0
a10=0
a9=0
1 2
- ---*a12*a3
2
a8=----------------
2
a1
- a12*a3
a7=-----------
a1
a6=0
a5=0
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:
b1,a3,a12,a1
Relevance for the application:
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3 2 2 1 4 2
df(u,t)=(u *a1 + f(v ,v )*a1 *a3 + f(v,v )*a1 *a3 - ---*f(v,v) *a12*a3
2x x x 2x 2
3 2
- f(v,v) *a1*a12*a3*u)/a1
1 3 2
---*f(v,v) *a12*a3*v + f(v,v) *a1*a12*u*v
2
df(v,t)=-------------------------------------------
a1
3 3 2
df(u,s)=(u *a1 *b1 - u *f(v,v) *a1*a12*a3*b1 + 3*f(v ,v )*a1 *a3*b1
4x 2x 2x 2x
2 3 2
+ 4*f(v ,v )*a1 *a3*b1 - f(v ,v )*f(v,v) *a12*a3 *b1
x 3x x x
2 3 2 3
+ f(v,v )*a1 *a3*b1 - f(v,v )*f(v,v) *a12*a3 *b1)/a1
4x 2x
2 2
df(v,s)=(u *f(v,v) *a1*a12*b1*v + f(v ,v )*f(v,v) *a12*a3*b1*v
2x x x
2 2
+ f(v,v )*f(v,v) *a12*a3*b1*v)/a1
2x