Solution 9 to problem l112o13
Expressions |
Parameters |
Relevance |
Back to problem l112o13
Expressions
The solution is given through the following expressions:
b42=0
b41=0
2 2
- 2*a0 *b23 - a0*a5*b39 + 2*a5 *b3
b40=-------------------------------------
a0*a5
b38=0
b37=0
b36=0
b35=0
1 1 2
---*a0*a3*b23 - ---*a0*a5*b21 - a5 *b31
2 4
b34=-----------------------------------------
2
a5
1 1
---*a0*a3*b23 - ---*a0*a5*b21
2 4
b33=-------------------------------
2
a5
2*a0*a3*b23 - a0*a5*b21
b32=-------------------------
2
a5
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b22=0
b20=0
b19=0
2*a5*b3
b18=---------
a0
2 2 2 3 2 2
- 2*a0 *a3 *b23 + a0 *a3*a5*b21 + 8*a0*a5 *b1 + a3 *a5 *b3
b17=-------------------------------------------------------------
2 2
a0 *a5
1 2 1 3
- ---*a0*a3 *b23 + ---*a0*a3*a5*b21 + 4*a5 *b1
2 4
b16=-------------------------------------------------
2
a0*a5
1 2 1 3
- ---*a0*a3 *b23 + ---*a0*a3*a5*b21 + 4*a5 *b1
2 4
b15=-------------------------------------------------
2
a0*a5
b14=0
b13=0
b12=0
b11=0
b10=0
2*a3*b3
b9=---------
a0
b8=0
a3*b1
b7=-------
a0
3*a3*b1
b6=---------
a0
b5=0
b4=0
b2=0
a8=0
a7=0
a4=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:
b39, b31, b23, b21, b3, b1, a3, a5, a0
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=u *a0 + u *a6 + f(v,v )*a3 + f(v,v) *a5
x x x
df(v,t)=v *a6
x
2 2 2 2 2 2
df(u,s)=(u *a0 *a5 *b1 + u *a0 *a5 *b3 + 2*u *f(v,v )*a0*a3*a5 *b3
3x x x x
2 3 2
+ 2*u *f(v,v) *a0*a5 *b3 + 3*f(v ,v )*a0*a3*a5 *b1
x x 2x
1 2 2 1 2
- ---*f(v ,v )*f(v,v)*a0 *a3 *b23 + ---*f(v ,v )*f(v,v)*a0 *a3*a5*b21
2 x x 4 x x
3 2
+ 4*f(v ,v )*f(v,v)*a0*a5 *b1 + f(v,v )*a0*a3*a5 *b1
x x 3x
1 2 2 1 2
- ---*f(v,v )*f(v,v)*a0 *a3 *b23 + ---*f(v,v )*f(v,v)*a0 *a3*a5*b21
2 2x 4 2x
3 2 2 2
+ 4*f(v,v )*f(v,v)*a0*a5 *b1 - 2*f(v,v ) *a0 *a3 *b23
2x x
2 2 2 3 2 2 2
+ f(v,v ) *a0 *a3*a5*b21 + 8*f(v,v ) *a0*a5 *b1 + f(v,v ) *a3 *a5 *b3
x x x
2 2 2 4 2 2 2 2
+ f(v,v )*f(v,v) *a0 *a5 *b21 + f(v,v) *a0 *a5 *b23)/(a0 *a5 )
x
2 2
df(v,s)=(v *f(v,v)*a0*a5 *b31 + 2*v *f(v,v )*a0 *a3*b23
2x x x
2 2 2
- v *f(v,v )*a0 *a5*b21 + v *f(v,v) *a0*a5 *b39
x x x
1 2 1 2
+ ---*f(v ,v )*a0 *a3*b23*v - ---*f(v ,v )*a0 *a5*b21*v
2 x x 4 x x
1 2 1 2
+ ---*f(v,v )*a0 *a3*b23*v - ---*f(v,v )*a0 *a5*b21*v
2 2x 4 2x
2 2
- f(v,v )*a0*a5 *b31*v - 2*f(v,v )*f(v,v)*a0 *a5*b23*v
2x x
2 3 2
- f(v,v )*f(v,v)*a0*a5 *b39*v + 2*f(v,v )*f(v,v)*a5 *b3*v)/(a0*a5 )
x x