Solution 10 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
4 1 4
- a0 *b23 + ----*a3 *b5
16
b42=--------------------------
3
a0 *a3
b41=0
3 2 1 3
- a0 *b21 - a0 *a3*b39 + ---*a3 *b4
4
b40=--------------------------------------
2
a0 *a3
b38=0
b37=0
b36=0
b35=0
2 1 2
- a0 *b16 - a0*a3*b31 + ---*a3 *b2
2
b34=-------------------------------------
a0*a3
2 1 2
- a0 *b15 + ---*a3 *b2
2
b33=-------------------------
a0*a3
2 2
- a0 *b17 + a3 *b3
b32=---------------------
a0*a3
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
1 3
---*a3 *b5
2
b22=------------
3
a0
3 2
---*a3 *b5
2
b20=------------
2
a0
2
a3 *b4
b19=--------
2
a0
1 2
---*a3 *b4
4
b18=------------
2
a0
2*a3*b5
b14=---------
a0
a3*b4
b13=-------
a0
a3*b4
b12=-------
a0
a3*b2
b11=-------
a0
a3*b2
b10=-------
a0
2*a3*b3
b9=---------
a0
1
---*a3*b2
2
b8=-----------
a0
a3*b1 - a3*b24
b7=----------------
a0
3*a3*b1
b6=---------
a0
a8=0
a7=0
a5=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, b24, b23, b21, b17, b16, b15, b5, b4, b3,
b2, b1, a3, a0
Relevance for the application:
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df(u,t)=u *a0 + u *a6 + f(v,v )*a3
x x x
df(v,t)=v *a6
x
3 1 2 3 2 3
df(u,s)=(u *a0 *b1 + ---*u *f(v,v)*a0 *a3*b2 + u *a0 *b2*u + u *a0 *b3
3x 2 2x 2x x
2 1 2 2
+ 2*u *f(v,v )*a0 *a3*b3 + ---*u *f(v,v) *a0*a3 *b4
x x 4 x
2 3 2 2
+ u *f(v,v)*a0 *a3*b4*u + u *a0 *b4*u + 3*f(v ,v )*a0 *a3*b1
x x x 2x
3 2 2
+ f(v ,v )*f(v,v)*a0 *b15 + f(v ,v )*a0 *a3*b2*u + f(v,v )*a0 *a3*b1
x x x x 3x
2 3
- f(v,v )*a0 *a3*b24 + f(v,v )*f(v,v)*a0 *b16
3x 2x
2 2 3 2 3
+ f(v,v )*a0 *a3*b2*u + f(v,v ) *a0 *b17 + f(v,v )*f(v,v) *a0 *b21
2x x x
2 2 2 4 3
+ f(v,v )*f(v,v)*a0*a3 *b4*u + f(v,v )*a0 *a3*b4*u + f(v,v) *a0 *b23
x x
1 3 3 3 2 2 2
+ ---*f(v,v) *a3 *b5*u + ---*f(v,v) *a0*a3 *b5*u
2 2
2 3 3 4 3
+ 2*f(v,v)*a0 *a3*b5*u + a0 *b5*u )/a0
3 3 4
df(v,s)=(v *a0 *a3*b24 + v *f(v,v)*a0 *a3*b31 - v *f(v,v )*a0 *b17
3x 2x x x
2 2 2 3 4
+ v *f(v,v )*a0 *a3 *b3 + v *f(v,v) *a0 *a3*b39 - f(v ,v )*a0 *b15*v
x x x x x
1 2 2 4
+ ---*f(v ,v )*a0 *a3 *b2*v - f(v,v )*a0 *b16*v
2 x x 2x
3 1 2 2
- f(v,v )*a0 *a3*b31*v + ---*f(v,v )*a0 *a3 *b2*v
2x 2 2x
4 3
- f(v,v )*f(v,v)*a0 *b21*v - f(v,v )*f(v,v)*a0 *a3*b39*v
x x
1 3 3 4
+ ---*f(v,v )*f(v,v)*a0*a3 *b4*v - f(v,v) *a0 *b23*v
4 x
1 3 4 3
+ ----*f(v,v) *a3 *b5*v)/(a0 *a3)
16