Solution 13 to problem l112o13
Expressions |
Parameters |
Relevance |
Back to problem l112o13
Expressions
The solution is given through the following expressions:
1 2
---*a5 *b38
4
b42=-------------
2
a8
- a5*b38
b41=-----------
a8
- a5*b35
b40=-----------
a8
1 2
---*a5 *b29
4
b39=-------------
2
a8
b37=0
- a5*b29
b36=-----------
a8
b34=0
b33=0
- a5*b26
b32=-----------
a8
b31=0
b30=0
b28=0
b27=0
b25=0
b24=0
1 4 1 3
----*a5 *b5 + ---*a5 *a8*b38
16 4
b23=------------------------------
4
a8
1 3 2
- ---*a5 *b5 - a5 *a8*b38
2
b22=----------------------------
3
a8
1 3 1 3 2
---*a5 *b29 - ---*a5 *b4 - a5 *a8*b35
4 4
b21=---------------------------------------
3
a8
3 2
---*a5 *b5 + a5*a8*b38
2
b20=------------------------
2
a8
2 2
- a5 *b29 + a5 *b4
b19=---------------------
2
a8
1 2
---*a5 *b4 + a5*a8*b35
4
b18=------------------------
2
a8
2 2
- a5 *b26 + a5 *b3
b17=---------------------
2
a8
1 2
---*a5 *b2
2
b16=------------
2
a8
1 2
---*a5 *b2
2
b15=------------
2
a8
- 2*a5*b5
b14=------------
a8
a5*b29 - a5*b4
b13=----------------
a8
- a5*b4
b12=----------
a8
- a5*b2
b11=----------
a8
- a5*b2
b10=----------
a8
a5*b26 - 2*a5*b3
b9=------------------
a8
1
- ---*a5*b2
2
b8=--------------
a8
- a5*b1
b7=----------
a8
- 3*a5*b1
b6=------------
a8
a7=0
a4=0
a3=0
a2=0
a0=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:
b38, b35, b29, b26, b5, b4, b3, b2, b1, a5, a8
Relevance for the application:
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2
df(u,t)=u *a6 + f(v,v) *a5
x
df(v,t)=v *a6 + f(v,v)*a8*v
x
4 1 3 4 2 4
df(u,s)=(u *a8 *b1 - ---*u *f(v,v)*a5*a8 *b2 + u *a8 *b2*u + u *a8 *b3
3x 2 2x 2x x
3 3
+ u *f(v,v )*a5*a8 *b26 - 2*u *f(v,v )*a5*a8 *b3
x x x x
1 2 2 2 2 3
+ ---*u *f(v,v) *a5 *a8 *b4 + u *f(v,v) *a5*a8 *b35
4 x x
3 4 2 3
- u *f(v,v)*a5*a8 *b4*u + u *a8 *b4*u - 3*f(v ,v )*a5*a8 *b1
x x x 2x
1 2 2 3
+ ---*f(v ,v )*f(v,v)*a5 *a8 *b2 - f(v ,v )*a5*a8 *b2*u
2 x x x x
3 1 2 2
- f(v,v )*a5*a8 *b1 + ---*f(v,v )*f(v,v)*a5 *a8 *b2
3x 2 2x
3 2 2 2 2 2 2
- f(v,v )*a5*a8 *b2*u - f(v,v ) *a5 *a8 *b26 + f(v,v ) *a5 *a8 *b3
2x x x
1 2 3 1 2 3
+ ---*f(v,v )*f(v,v) *a5 *a8*b29 - ---*f(v,v )*f(v,v) *a5 *a8*b4
4 x 4 x
2 2 2 2 2
- f(v,v )*f(v,v) *a5 *a8 *b35 - f(v,v )*f(v,v)*a5 *a8 *b29*u
x x
2 2 3 2
+ f(v,v )*f(v,v)*a5 *a8 *b4*u + f(v,v )*a5*a8 *b29*u
x x
3 2 1 4 4 1 4 3
- f(v,v )*a5*a8 *b4*u + ----*f(v,v) *a5 *b5 + ---*f(v,v) *a5 *a8*b38
x 16 4
1 3 3 3 2 2
- ---*f(v,v) *a5 *a8*b5*u - f(v,v) *a5 *a8 *b38*u
2
3 2 2 2 2 2 3 2
+ ---*f(v,v) *a5 *a8 *b5*u + f(v,v) *a5*a8 *b38*u
2
3 3 4 4 4
- 2*f(v,v)*a5*a8 *b5*u + a8 *b5*u )/a8
2 2
df(v,s)=(u *v *a8 *b26 + u *f(v,v)*a8 *b35*v - v *f(v,v )*a5*a8*b26
x x x x x
1 2 2 2 2
+ ---*v *f(v,v) *a5 *b29 - v *f(v,v)*a5*a8*b29*u + v *a8 *b29*u
4 x x x
1 3 2
- f(v,v )*f(v,v)*a5*a8*b35*v + ---*f(v,v) *a5 *b38*v
x 4
2 2 2 2
- f(v,v) *a5*a8*b38*u*v + f(v,v)*a8 *b38*u *v)/a8