Solution 2 to problem l2313o24
Expressions |
Parameters |
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Back to problem l2313o24
Expressions
The solution is given through the following expressions:
1 2 6
----*a10 *a4 *b34
64
b66=-------------------
8
a9
3 2 5
- ----*a10 *a4 *b34
16
b65=----------------------
7
a9
15 2 4
----*a10 *a4 *b34
16
b64=-------------------
6
a9
5 2 3
- ---*a10 *a4 *b34
2
b63=---------------------
5
a9
3
- 3*a10*a4 *b34
b62=------------------
4
a9
3 3
- ---*a10*a4 *b34
4
b61=--------------------
4
a9
3 3
- ---*a10*a4 *b34
4
b60=--------------------
4
a9
3 3
- ---*a10*a4 *b34
2
b59=--------------------
4
a9
1 3
- ---*a10*a4 *b34
4
b58=--------------------
4
a9
15 2 2
----*a10 *a4 *b34
4
b57=-------------------
4
a9
2
6*a10*a4 *b34
b56=---------------
3
a9
2
3*a10*a4 *b34
b55=---------------
3
a9
2
3*a10*a4 *b34
b54=---------------
3
a9
2
6*a10*a4 *b34
b53=---------------
3
a9
3 2
---*a10*a4 *b34
2
b52=-----------------
3
a9
2
6*a10*a4 *b34
b51=---------------
3
a9
3 2
---*a10*a4 *b34
2
b50=-----------------
3
a9
3 2
---*a10*a4 *b34
4
b49=-----------------
3
a9
2
- 3*a10 *a4*b34
b48=------------------
3
a9
- 3*a10*a4*b34
b47=-----------------
2
a9
- 3*a10*a4*b34
b46=-----------------
2
a9
- 6*a10*a4*b34
b45=-----------------
2
a9
- 3*a10*a4*b34
b44=-----------------
2
a9
- 12*a10*a4*b34
b43=------------------
2
a9
- 6*a10*a4*b34
b42=-----------------
2
a9
- 3*a10*a4*b34
b41=-----------------
2
a9
- 3*a10*a4*b34
b40=-----------------
2
a9
2
a10 *b34
b39=----------
2
a9
2*a10*b34
b38=-----------
a9
6*a10*b34
b37=-----------
a9
6*a10*b34
b36=-----------
a9
3*a10*b34
b35=-----------
a9
1 2 7
----*a10 *a4 *b34
64
b33=-------------------
9
a9
3 2 6
- ----*a10 *a4 *b34
16
b32=----------------------
8
a9
15 2 5
----*a10 *a4 *b34
16
b31=-------------------
7
a9
5 2 4
- ---*a10 *a4 *b34
2
b30=---------------------
6
a9
9 4
- ---*a10*a4 *b34
2
b29=--------------------
5
a9
4
- a10*a4 *b34
b28=----------------
5
a9
3 4
- ---*a10*a4 *b34
4
b27=--------------------
5
a9
15 2 3
----*a10 *a4 *b34
4
b26=-------------------
5
a9
3
12*a10*a4 *b34
b25=----------------
4
a9
9 3
---*a10*a4 *b34
2
b24=-----------------
4
a9
3
3*a10*a4 *b34
b23=---------------
4
a9
15 3
----*a10*a4 *b34
2
b22=------------------
4
a9
3 3
---*a10*a4 *b34
4
b21=-----------------
4
a9
2 2
- 3*a10 *a4 *b34
b20=-------------------
4
a9
2
- 6*a10*a4 *b34
b19=------------------
3
a9
2
- 6*a10*a4 *b34
b18=------------------
3
a9
2
- 3*a10*a4 *b34
b17=------------------
3
a9
2
- 18*a10*a4 *b34
b16=-------------------
3
a9
2
- 3*a10*a4 *b34
b15=------------------
3
a9
2
- 3*a10*a4 *b34
b14=------------------
3
a9
2
a10 *a4*b34
b13=-------------
3
a9
2*a10*a4*b34
b12=--------------
2
a9
b11=0
6*a10*a4*b34
b10=--------------
2
a9
6*a10*a4*b34
b9=--------------
2
a9
3*a10*a4*b34
b8=--------------
2
a9
a4*b34
b7=--------
a9
b6=0
b5=0
b4=0
b3=0
b2=0
b1=0
1 3
- ---*a10*a4
8
a13=----------------
3
a9
3 2
---*a10*a4
4
a12=-------------
2
a9
3
- ---*a10*a4
2
a11=---------------
a9
1 4
- ---*a10*a4
8
a8=----------------
4
a9
3 3
---*a10*a4
4
a7=-------------
3
a9
3 2
- ---*a10*a4
2
a6=----------------
2
a9
a10*a4
a5=--------
a9
a3=0
a2=0
a1=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:
b34,a4,a10,a9
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
4 1 4 4 3 3 3
df(u,t)=(f(v,v )*a4*a9 - ---*f(v,v) *a10*a4 + ---*f(v,v) *a10*a4 *a9*u
2x 8 4
3 2 2 2 2 3 3 4
- ---*f(v,v) *a10*a4 *a9 *u + f(v,v)*a10*a4*a9 *u )/a9
2
4 1 3 3 3 2 2
df(v,t)=(v *a9 - ---*f(v,v) *a10*a4 *v + ---*f(v,v) *a10*a4 *a9*u*v
2x 8 4
3 2 2 3 3 3
- ---*f(v,v)*a10*a4*a9 *u *v + a10*a9 *u *v)/a9
2
3 3 3 5 2 2 6
df(u,s)=(---*u *f(v,v) *a10*a4 *a9 *b34 - 3*u *f(v,v) *a10*a4 *a9 *b34*u
4 2x 2x
7 2 2 2 2 6
+ 3*u *f(v,v)*a10*a4*a9 *b34*u - 3*u *f(v,v) *a10*a4 *a9 *b34
2x x
2 7
+ 6*u *f(v,v)*a10*a4*a9 *b34*u
x
15 2 3 5
+ ----*u *f(v,v )*f(v,v) *a10*a4 *a9 *b34
2 x x
2 6
- 18*u *f(v,v )*f(v,v)*a10*a4 *a9 *b34*u
x x
7 2
+ 6*u *f(v,v )*a10*a4*a9 *b34*u
x x
3 3 4 4
- ---*f(v ,v )*f(v,v) *a10*a4 *a9 *b34
4 x x
2 3 5
+ 3*f(v ,v )*f(v,v) *a10*a4 *a9 *b34*u
x x
2 6 2 8
- 3*f(v ,v )*f(v,v)*a10*a4 *a9 *b34*u + f(v,v )*a4*a9 *b34
x x 4x
3 4 4
- f(v,v )*f(v,v) *a10*a4 *a9 *b34
2x
9 2 3 5
+ ---*f(v,v )*f(v,v) *a10*a4 *a9 *b34*u
2 2x
2 6 2 7 3
- 6*f(v,v )*f(v,v)*a10*a4 *a9 *b34*u + 2*f(v,v )*a10*a4*a9 *b34*u
2x 2x
9 2 2 4 4
- ---*f(v,v ) *f(v,v) *a10*a4 *a9 *b34
2 x
2 3 5 2 2 6 2
+ 12*f(v,v ) *f(v,v)*a10*a4 *a9 *b34*u - 6*f(v,v ) *a10*a4 *a9 *b34*u
x x
1 7 2 7 3 6 2 6
+ ----*f(v,v) *a10 *a4 *b34 - ----*f(v,v) *a10 *a4 *a9*b34*u
64 16
15 5 2 5 2 2 5 4 2 4 3 3
+ ----*f(v,v) *a10 *a4 *a9 *b34*u - ---*f(v,v) *a10 *a4 *a9 *b34*u
16 2
15 3 2 3 4 4 2 2 2 5 5
+ ----*f(v,v) *a10 *a4 *a9 *b34*u - 3*f(v,v) *a10 *a4 *a9 *b34*u
4
2 6 6 9
+ f(v,v)*a10 *a4*a9 *b34*u )/a9
3 2 2 5 6
df(v,s)=(---*u *f(v,v) *a10*a4 *a9 *b34*v - 3*u *f(v,v)*a10*a4*a9 *b34*u*v
4 2x 2x
7 2 2 6
+ 3*u *a10*a9 *b34*u *v - 3*u *f(v,v)*a10*a4*a9 *b34*v
2x x
2 7 3 2 2 5
+ 6*u *a10*a9 *b34*u*v + ---*u *v *f(v,v) *a10*a4 *a9 *b34
x 2 x x
6 7 2
- 6*u *v *f(v,v)*a10*a4*a9 *b34*u + 6*u *v *a10*a9 *b34*u
x x x x
2 5
+ 6*u *f(v,v )*f(v,v)*a10*a4 *a9 *b34*v
x x
6 8
- 12*u *f(v,v )*a10*a4*a9 *b34*u*v + v *a9 *b34
x x 4x
1 3 3 4 3 2 2 5
- ---*v *f(v,v) *a10*a4 *a9 *b34 + ---*v *f(v,v) *a10*a4 *a9 *b34*u
4 2x 2 2x
6 2 7 3
- 3*v *f(v,v)*a10*a4*a9 *b34*u + 2*v *a10*a9 *b34*u
2x 2x
3 2 3 4
- ---*v *f(v,v )*f(v,v) *a10*a4 *a9 *b34
2 x x
2 5
+ 6*v *f(v,v )*f(v,v)*a10*a4 *a9 *b34*u
x x
6 2
- 6*v *f(v,v )*a10*a4*a9 *b34*u
x x
3 2 3 4
- ---*f(v ,v )*f(v,v) *a10*a4 *a9 *b34*v
4 x x
2 5
+ 3*f(v ,v )*f(v,v)*a10*a4 *a9 *b34*u*v
x x
6 2
- 3*f(v ,v )*a10*a4*a9 *b34*u *v
x x
3 2 3 4
- ---*f(v,v )*f(v,v) *a10*a4 *a9 *b34*v
4 2x
2 5
+ 3*f(v,v )*f(v,v)*a10*a4 *a9 *b34*u*v
2x
6 2 2 3 4
- 3*f(v,v )*a10*a4*a9 *b34*u *v - 3*f(v,v ) *f(v,v)*a10*a4 *a9 *b34*v
2x x
2 2 5 1 6 2 6
+ 6*f(v,v ) *a10*a4 *a9 *b34*u*v + ----*f(v,v) *a10 *a4 *b34*v
x 64
3 5 2 5
- ----*f(v,v) *a10 *a4 *a9*b34*u*v
16
15 4 2 4 2 2
+ ----*f(v,v) *a10 *a4 *a9 *b34*u *v
16
5 3 2 3 3 3
- ---*f(v,v) *a10 *a4 *a9 *b34*u *v
2
15 2 2 2 4 4 2 5 5
+ ----*f(v,v) *a10 *a4 *a9 *b34*u *v - 3*f(v,v)*a10 *a4*a9 *b34*u *v
4
2 6 6 8
+ a10 *a9 *b34*u *v)/a9