Solution 1 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
1 2 2 1 2 2
---*a0 *a3 *a8*b28 - ---*a3 *a7 *a8*b1
4 2
b42=----------------------------------------
5
a0
3 1 2 2 2 1 2 3
a0 *a3*a8*b28 + ---*a0 *a3 *a7*b28 - 2*a0*a3*a7 *a8*b1 - ---*a3 *a7 *b1
4 2
b41=-------------------------------------------------------------------------
5
a0
1 2 2 2 2
---*a0 *a3 *b28 + 2*a0*a3*a7*a8*b1 - a3 *a7 *b1
2
b40=-------------------------------------------------
4
a0
b39=0
3 2 2 3
a0 *a8*b28 + a0 *a3*a7*b28 - 2*a0*a7 *a8*b1 - 2*a3*a7 *b1
b38=-----------------------------------------------------------
4
a0
a3*b28
b37=--------
a0
b36=0
1 2 2
---*a0 *a3*b28 + 2*a0*a7*a8*b1 - a3*a7 *b1
2
b35=--------------------------------------------
3
a0
a3*a7*b1
b34=----------
2
a0
a3*a7*b1
b33=----------
2
a0
b32=0
b31=0
2 3
a0 *a7*b28 - 2*a7 *b1
b30=-----------------------
3
a0
b29=0
b27=0
b26=0
a7*b1
b25=-------
a0
b24=0
1 2 3 1 3 2
- ---*a0 *a3 *a8*b28 + ---*a3 *a7 *a8*b1
4 2
b23=-------------------------------------------
6
a0
1 2 3 2 1 3 2
---*a0 *a3 *b28 - 2*a0*a3 *a7*a8*b1 - ---*a3 *a7 *b1
4 2
b21=------------------------------------------------------
5
a0
3 2 2 2 2 3
- a0 *a3*a8*b28 - a0 *a3 *a7*b28 + 2*a0*a3*a7 *a8*b1 + 2*a3 *a7 *b1
b20=----------------------------------------------------------------------
5
a0
2 2 2 2
2*a0 *a3 *b28 - 6*a3 *a7 *b1
b19=------------------------------
4
a0
1 2 2 1 2 2
---*a0 *a3 *b28 - 2*a0*a3*a7*a8*b1 - ---*a3 *a7 *b1
4 2
b18=-----------------------------------------------------
4
a0
2
a3 *b28
b17=---------
a0*a7
1 2 2 2 2
---*a0 *a3 *b28 - a3 *a7 *b1
2
b16=------------------------------
3
a0 *a7
1 2 2 2 2
---*a0 *a3 *b28 - a3 *a7 *b1
2
b15=------------------------------
3
a0 *a7
2 3
- a0 *a3*a7*b28 + 2*a3*a7 *b1
b14=--------------------------------
4
a0
2 2
3*a0 *a3*b28 - 6*a3*a7 *b1
b13=----------------------------
3
a0
2 2
2*a0 *a3*b28 - 6*a3*a7 *b1
b12=----------------------------
3
a0
a3*b28
b11=--------
a7
a3*b28
b10=--------
a7
2*a3*b28
b9=----------
a7
1 2 2
---*a0 *a3*b28 - a3*a7 *b1
2
b8=----------------------------
2
a0 *a7
a3*b1
b7=-------
a0
3*a3*b1
b6=---------
a0
b5=0
2 2
3*a0 *b28 - 6*a7 *b1
b4=----------------------
2
a0
a0*b28
b3=--------
a7
a0*b28
b2=--------
a7
- a3*a8
a5=----------
a0
- a3*a7
a4=----------
a0
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:
b22, b1, b28, a8, a3, a0, a7, a6
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 2
u *a0 + u *a0*a6 + f(v,v )*a0*a3 - f(v,v) *a3*a8 - f(v,v)*a3*a7*u
x x x
df(u,t)=--------------------------------------------------------------------
a0
df(v,t)=v *a6 + f(v,v)*a8*v + a7*u*v
x
6 1 6 4 2
df(u,s)=(u *a0 *a7*b1 + ---*u *f(v,v)*a0 *a3*b28 - u *f(v,v)*a0 *a3*a7 *b1
3x 2 2x 2x
7 2 7 6
+ u *a0 *b28*u + u *a0 *b28 + 2*u *f(v,v )*a0 *a3*b28
2x x x x
1 2 4 2 2 3 2
+ ---*u *f(v,v) *a0 *a3 *a7*b28 - 2*u *f(v,v) *a0 *a3*a7 *a8*b1
4 x x
1 2 2 2 3 5
- ---*u *f(v,v) *a0 *a3 *a7 *b1 + 2*u *f(v,v)*a0 *a3*a7*b28*u
2 x x
3 3 6 2
- 6*u *f(v,v)*a0 *a3*a7 *b1*u + 3*u *a0 *a7*b28*u
x x
4 3 2 5
- 6*u *a0 *a7 *b1*u + 3*f(v ,v )*a0 *a3*a7*b1
x x 2x
1 5 2 3 2 2
+ ---*f(v ,v )*f(v,v)*a0 *a3 *b28 - f(v ,v )*f(v,v)*a0 *a3 *a7 *b1
2 x x x x
6 5
+ f(v ,v )*a0 *a3*b28*u + f(v,v )*a0 *a3*a7*b1
x x 3x
1 5 2 3 2 2
+ ---*f(v,v )*f(v,v)*a0 *a3 *b28 - f(v,v )*f(v,v)*a0 *a3 *a7 *b1
2 2x 2x
6 2 5 2
+ f(v,v )*a0 *a3*b28*u + f(v,v ) *a0 *a3 *b28
2x x
1 2 3 3
+ ---*f(v,v )*f(v,v) *a0 *a3 *a7*b28
4 x
2 2 2 2
- 2*f(v,v )*f(v,v) *a0 *a3 *a7 *a8*b1
x
1 2 3 3
- ---*f(v,v )*f(v,v) *a0*a3 *a7 *b1
2 x
4 2
+ 2*f(v,v )*f(v,v)*a0 *a3 *a7*b28*u
x
2 2 3 5 2
- 6*f(v,v )*f(v,v)*a0 *a3 *a7 *b1*u + 3*f(v,v )*a0 *a3*a7*b28*u
x x
3 3 2 1 4 2 3
- 6*f(v,v )*a0 *a3*a7 *b1*u - ---*f(v,v) *a0 *a3 *a7*a8*b28
x 4
1 4 3 3 3 6
+ ---*f(v,v) *a3 *a7 *a8*b1 + f(v,v) *a0 *a7*b22*u
2
2 4 2 2 3 2 2 2
- f(v,v) *a0 *a3*a7*a8*b28*u - f(v,v) *a0 *a3 *a7 *b28*u
2 2 3 2 2 2 4 2
+ 2*f(v,v) *a0 *a3*a7 *a8*b1*u + 2*f(v,v) *a0*a3 *a7 *b1*u
4 2 3 2 4 3 6
- f(v,v)*a0 *a3*a7 *b28*u + 2*f(v,v)*a0 *a3*a7 *b1*u )/(a0 *a7)
4 1 4
df(v,s)=(u *a0 *a7*b1*v + ---*u *f(v,v)*a0 *a3*b28*v
2x 2 x
3 2 2
+ 2*u *f(v,v)*a0 *a7*a8*b1*v - u *f(v,v)*a0 *a3*a7 *b1*v
x x
5 3 3
+ u *a0 *b28*u*v + f(v ,v )*a0 *a3*a7*b1*v + f(v,v )*a0 *a3*a7*b1*v
x x x 2x
1 3 2
+ ---*f(v,v )*f(v,v)*a0 *a3 *b28*v
2 x
2 2 2
+ 2*f(v,v )*f(v,v)*a0 *a3*a7*a8*b1*v - f(v,v )*f(v,v)*a0*a3 *a7 *b1*v
x x
4 1 3 2 2
+ f(v,v )*a0 *a3*b28*u*v + ---*f(v,v) *a0 *a3 *a8*b28*v
x 4
1 3 2 2 2 3
- ---*f(v,v) *a3 *a7 *a8*b1*v + f(v,v) *a0 *a3*a8*b28*u*v
2
1 2 2 2 2 2
+ ---*f(v,v) *a0 *a3 *a7*b28*u*v - 2*f(v,v) *a0*a3*a7 *a8*b1*u*v
4
1 2 2 3 4 2
- ---*f(v,v) *a3 *a7 *b1*u*v + f(v,v)*a0 *a8*b28*u *v
2
3 2 2 2 2
+ f(v,v)*a0 *a3*a7*b28*u *v - 2*f(v,v)*a0 *a7 *a8*b1*u *v
3 2 4 3 2 3 3
- 2*f(v,v)*a0*a3*a7 *b1*u *v + a0 *a7*b28*u *v - 2*a0 *a7 *b1*u *v)/
5
a0