Solution 32 to problem l112o23
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Parameters |
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Expressions
The solution is given through the following expressions:
b42=0
b41=0
b40=0
b39=0
b38=0
b37=0
b36=0
b35=0
3
- ---*a13*a5*b24
4
b34=-------------------
2
a12
3
- ---*a13*a5*b24
4
b33=-------------------
2
a12
3
- ---*a13*a5*b24
2
b32=-------------------
2
a12
b31=0
b30=0
b29=0
b28=0
b27=0
3
---*a13*b24
2
b26=-------------
a12
3
---*a13*b24
4
b25=-------------
a12
b23=0
b22=0
b21=0
b20=0
b19=0
b18=0
3 2
- ---*a13*a5 *b24
4
b17=--------------------
3
a12
3 2
- ---*a13*a5 *b24
4
b16=--------------------
3
a12
3 2
- ---*a13*a5 *b24
4
b15=--------------------
3
a12
b14=0
b13=0
b12=0
b11=0
b10=0
b9=0
3
---*a13*a5*b24
4
b8=----------------
2
a12
3
---*a5*b24
4
b7=------------
a12
3
- ---*a5*b24
4
b6=---------------
a12
b5=0
b4=0
3
---*a13*b24
4
b3=-------------
a12
b2=0
1
b1=---*b24
4
a19=0
a18=0
- a13*a5
a17=-----------
a12
a16=0
a15=0
a14=0
a11=0
a10=0
2
- a13*a5
a9=------------
2
a12
a8=0
a7=0
a13*a5
a6=--------
a12
a4=0
a3=0
a2=0
a1=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:
b24,a5,a13,a12
Relevance for the application:
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2 2
u *f(v,v)*a12*a13*a5 + f(v,v )*a12 *a5 - f(v,v )*f(v,v)*a13*a5
x 2x x
df(u,t)=------------------------------------------------------------------
2
a12
2
u *a12*a13*v + v *a12 - f(v,v )*a13*a5*v
x 2x x
df(v,t)=--------------------------------------------
a12
1 3 3 3 2 2
df(u,s)=(---*u *a12 *b24 + ---*u *f(v,v)*a12*a13*a5*b24 + ---*u *a12 *a13*b24
4 3x 4 2x 4 x
3 2 3 2
- ---*f(v ,v )*a12 *a5*b24 - ---*f(v ,v )*f(v,v)*a13*a5 *b24
4 x 2x 4 x x
3 2 3 2
+ ---*f(v,v )*a12 *a5*b24 - ---*f(v,v )*f(v,v)*a13*a5 *b24
4 3x 4 2x
3 2 2 3
- ---*f(v,v ) *a13*a5 *b24)/a12
4 x
3 3 2
df(v,s)=(---*u *a12*a13*b24*v + ---*u *v *a12*a13*b24 + v *a12 *b24
4 2x 2 x x 3x
3 3
- ---*v *f(v,v )*a13*a5*b24 - ---*f(v ,v )*a13*a5*b24*v
2 x x 4 x x
3 2
- ---*f(v,v )*a13*a5*b24*v)/a12
4 2x