Solution 13 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
3 5 2 49 2 2
- 6*a1 *a9*b16 + ---*a1 *a3*a9*b30 - ----*a3 *a9 *b1
9 9
b40=-------------------------------------------------------
4
a1
3 5 2 49 2 2
a1 *a9*b16 - ---*a1 *a3*a9*b30 + ----*a3 *a9 *b1
9 54
b39=--------------------------------------------------
4
a1
3 10 2 50 2 2
- 18*a1 *a9*b16 + ----*a1 *a3*a9*b30 - ----*a3 *a9 *b1
3 3
b38=---------------------------------------------------------
3
a1 *a3
3 10 2 50 2 2
6*a1 *a9*b16 - ----*a1 *a3*a9*b30 + ----*a3 *a9 *b1
3 9
b37=-----------------------------------------------------
3
a1 *a3
3 25 2 2
- 9*a1 *a9*b16 - ----*a3 *a9 *b1
3
b36=-----------------------------------
3
a1 *a3
3 2 25 2
9*a1 *b16 - a1 *a3*b30 + ----*a3 *a9*b1
3
b35=-----------------------------------------
2
a1 *a3
3 5 2
- 3*a1 *b16 - ---*a3 *a9*b1
3
b34=------------------------------
2
a1 *a3
3 2 50 2
- 6*a1 *b16 + a1 *a3*b30 - ----*a3 *a9*b1
9
b33=--------------------------------------------
2
a1 *a3
3 10 2
4*a1 *b16 + ----*a3 *a9*b1
3
b32=----------------------------
2
a1 *a3
b31= - b30
2 2
---*a9 *b1
3
b29=------------
2
a1
2
- 2*a9 *b1
b28=-------------
2
a1
b27=0
b26=0
2
- ---*a9*b1
3
b25=--------------
a1
a9*b1
b24=-------
a1
b23=0
5 3 125 3 2
---*a1 *a3*a9*b16 + -----*a3 *a9 *b1
3 81
b22=--------------------------------------
5
a1
3 110 2 2
4*a1 *a9*b16 + -----*a3 *a9 *b1
27
b21=---------------------------------
4
a1
3 155 2 2
3*a1 *a9*b16 + -----*a3 *a9 *b1
54
b20=---------------------------------
4
a1
3 10 2
2*a1 *b16 + ----*a3 *a9*b1
9
b19=----------------------------
3
a1
3 80 2
- 3*a1 *b16 - ----*a3 *a9*b1
27
b18=-------------------------------
3
a1
4 3 50 2
- ---*a1 *b16 - ----*a3 *a9*b1
3 27
b17=---------------------------------
3
a1
8 2
---*a3*a9 *b1
9
b15=---------------
3
a1
16 2
----*a3*a9 *b1
9
b14=----------------
3
a1
10
- ----*a3*a9*b1
9
b13=------------------
2
a1
10
- ----*a3*a9*b1
3
b12=------------------
2
a1
20
- ----*a3*a9*b1
9
b11=------------------
2
a1
20
- ----*a3*a9*b1
9
b10=------------------
2
a1
- 2*a3*a9*b1
b9=---------------
2
a1
8
- ---*a3*a9*b1
9
b8=-----------------
2
a1
1
---*a3*b1
3
b7=-----------
a1
5
---*a3*b1
3
b6=-----------
a1
10
----*a3*b1
3
b5=------------
a1
10 2
----*a9 *b1
3
b4=-------------
2
a1
20
- ----*a9*b1
3
b3=---------------
a1
10
- ----*a9*b1
3
b2=---------------
a1
1
---*a3*a9
3
a12=-----------
a1
1
- ---*a3*a9
9
a11=--------------
a1
2
a10= - ---*a9
3
a8=0
5 2
- ----*a3 *a9
27
a7=----------------
2
a1
4
- ---*a3*a9
9
a6=--------------
a1
2
- ---*a3*a9
3
a5=--------------
a1
1
a4=---*a3
3
a2= - 2*a9
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:
b16,b30,b1,a3,a9,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 2 2
df(u,t)=(u *a1 - ---*u *f(v,v)*a1*a3*a9 - 2*u *a1 *a9*u + f(v ,v )*a1 *a3
3x 3 x x x 2x
1 2 5 2
+ ---*f(v,v )*a1 *a3 - ----*f(v,v )*f(v,v)*a3 *a9
3 3x 27 x
4 2
- ---*f(v,v )*a1*a3*a9*u)/a1
9 x
df(v,t)=
1 2 1
u *a1*a9*v - ---*v *f(v,v)*a3*a9 - ---*v *a1*a9*u + ---*f(v,v )*a3*a9*v
x 9 x 3 x 3 x
-------------------------------------------------------------------------
a1
5 8 3 10 4
df(u,s)=(u *a1 *b1 - ---*u *f(v,v)*a1 *a3*a9*b1 - ----*u *a1 *a9*b1*u
5x 9 3x 3 3x
20 4 3
- ----*u *u *a1 *a9*b1 - 2*u *f(v,v )*a1 *a3*a9*b1
3 2x x 2x x
20 3 20 3
- ----*u *f(v ,v )*a1 *a3*a9*b1 - ----*u *f(v,v )*a1 *a3*a9*b1
9 x x x 9 x 2x
2 4 155 2 2 2
+ 3*u *f(v,v) *a1 *a9*b16 + -----*u *f(v,v) *a1*a3 *a9 *b1
x 54 x
16 2 2 10 3 2 2
+ ----*u *f(v,v)*a1 *a3*a9 *b1*u + ----*u *a1 *a9 *b1*u
9 x 3 x
10 4 5 4
+ ----*f(v ,v )*a1 *a3*b1 + ---*f(v ,v )*a1 *a3*b1
3 2x 3x 3 x 4x
5 10 3
+ f(v ,v )*f(v,v)*a1 *b16 - ----*f(v ,v )*a1 *a3*a9*b1*u
x 2x 3 x 2x
4 5 50 2 2
- ---*f(v ,v )*f(v,v )*a1 *b16 - ----*f(v ,v )*f(v,v )*a1 *a3 *a9*b1
3 x x x 27 x x x
1 4 5
+ ---*f(v,v )*a1 *a3*b1 - 3*f(v,v )*f(v,v)*a1 *b16
3 5x 3x
80 2 2 10 3
- ----*f(v,v )*f(v,v)*a1 *a3 *a9*b1 - ----*f(v,v )*a1 *a3*a9*b1*u
27 3x 9 3x
5 10 2 2
+ 2*f(v,v )*f(v,v )*a1 *b16 + ----*f(v,v )*f(v,v )*a1 *a3 *a9*b1
2x x 9 2x x
5 2 3 125 2 3 2
+ ---*f(v,v )*f(v,v) *a1 *a3*a9*b16 + -----*f(v,v )*f(v,v) *a3 *a9 *b1
3 x 81 x
4 110 2 2
+ 4*f(v,v )*f(v,v)*a1 *a9*b16*u + -----*f(v,v )*f(v,v)*a1*a3 *a9 *b1*u
x 27 x
8 2 2 2 5
+ ---*f(v,v )*a1 *a3*a9 *b1*u )/a1
9 x
3 2 3 4
df(v,s)=(u *a1 *a3*a9*b1*v - ---*u *v *a1 *a3*a9*b1 - 9*u *f(v,v)*a1 *a9*b16*v
3x 3 2x x x
25 2 2 2 2
- ----*u *f(v,v)*a1*a3 *a9 *b1*v - 2*u *a1 *a3*a9 *b1*u*v
3 x x
4 4
+ v *f(v,v)*a1 *a3*b30 - v *f(v,v )*a1 *a3*b30
3x 2x x
5 10 2 2
+ 4*v *f(v ,v )*a1 *b16 + ----*v *f(v ,v )*a1 *a3 *a9*b1
x x x 3 x x x
5 4
- 6*v *f(v,v )*a1 *b16 + v *f(v,v )*a1 *a3*b30
x 2x x 2x
50 2 2 2 3
- ----*v *f(v,v )*a1 *a3 *a9*b1 + v *f(v,v) *a1 *a3*a9*b16
9 x 2x x
5 2 2 2 49 2 3 2
- ---*v *f(v,v) *a1 *a3 *a9*b30 + ----*v *f(v,v) *a3 *a9 *b1
9 x 54 x
4 10 3
+ 6*v *f(v,v)*a1 *a9*b16*u - ----*v *f(v,v)*a1 *a3*a9*b30*u
x 3 x
50 2 2 2 2 2 2
+ ----*v *f(v,v)*a1*a3 *a9 *b1*u + ---*v *a1 *a3*a9 *b1*u
9 x 3 x
5 5 2 2
- 3*f(v ,v )*a1 *b16*v - ---*f(v ,v )*a1 *a3 *a9*b1*v
x 2x 3 x 2x
5 4
+ 9*f(v,v )*a1 *b16*v - f(v,v )*a1 *a3*b30*v
3x 3x
25 2 2 3
+ ----*f(v,v )*a1 *a3 *a9*b1*v - 6*f(v,v )*f(v,v)*a1 *a3*a9*b16*v
3 3x x
5 2 2
+ ---*f(v,v )*f(v,v)*a1 *a3 *a9*b30*v
9 x
49 3 2 4
- ----*f(v,v )*f(v,v)*a3 *a9 *b1*v - 18*f(v,v )*a1 *a9*b16*u*v
9 x x
10 3 50 2 2
+ ----*f(v,v )*a1 *a3*a9*b30*u*v - ----*f(v,v )*a1*a3 *a9 *b1*u*v)/(
3 x 3 x
4
a1 *a3)