Solution 4 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
5 2 2
----*a2 *a4 *b23
81
b40=------------------
4
a8
b39=0
25 2
----*a2 *a4*b23
27
b38=-----------------
3
a8
5 2
----*a2 *a4*b23
27
b37=-----------------
3
a8
10 2
----*a2 *a4*b23
27
b36=-----------------
3
a8
10
----*a2*a4*b23
9
b35=----------------
2
a8
20
----*a2*a4*b23
9
b34=----------------
2
a8
10
----*a2*a4*b23
9
b33=----------------
2
a8
5
---*a2*a4*b23
6
b32=---------------
2
a8
5
---*a2*a4*b23
9
b31=---------------
2
a8
b30=0
5 2
---*a2 *b23
6
b29=-------------
2
a8
5 2
---*a2 *b23
3
b28=-------------
2
a8
5
---*a2*b23
3
b27=------------
a8
10
----*a2*b23
3
b26=-------------
a8
10
----*a2*b23
3
b25=-------------
a8
5
---*a2*b23
3
b24=------------
a8
b22=0
20 2 2
----*a2 *a4 *b23
81
b21=------------------
4
a8
5 2 2
----*a2 *a4 *b23
81
b20=------------------
4
a8
35 2
----*a2*a4 *b23
27
b19=-----------------
3
a8
10 2
----*a2*a4 *b23
27
b18=-----------------
3
a8
10 2
----*a2*a4 *b23
9
b17=-----------------
3
a8
25 2
----*a2*a4 *b23
27
b16=-----------------
3
a8
10 2
----*a2 *a4*b23
9
b15=-----------------
3
a8
10 2
----*a2 *a4*b23
9
b14=-----------------
3
a8
25
----*a2*a4*b23
9
b13=----------------
2
a8
50
----*a2*a4*b23
9
b12=----------------
2
a8
50
----*a2*a4*b23
9
b11=----------------
2
a8
25
----*a2*a4*b23
6
b10=----------------
2
a8
5*a2*a4*b23
b9=-------------
2
a8
10
----*a2*a4*b23
9
b8=----------------
2
a8
5
---*a4*b23
3
b7=------------
a8
5*a4*b23
b6=----------
a8
25
----*a4*b23
3
b5=-------------
a8
5 2
---*a2 *b23
6
b4=-------------
2
a8
10
----*a2*b23
3
b3=-------------
a8
5
---*a2*b23
3
b2=------------
a8
b1=b23
1
---*a2*a4
3
a12=-----------
a8
a11=0
a10=a2
a9=a2
a7=0
2
---*a2*a4
3
a6=-----------
a8
1
---*a2*a4
3
a5=-----------
a8
a3=2*a4
a1=a8
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:
b23,a4,a2,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 1
df(u,t)=(u *a8 + ---*u *f(v,v)*a2*a4 + u *a2*a8*u + 2*f(v ,v )*a4*a8
3x 3 x x x 2x
2
+ f(v,v )*a4*a8 + ---*f(v,v )*a2*a4*u)/a8
3x 3 x
2 1
u *a2*a8*v + v *a8 + v *a2*a8*u + ---*f(v,v )*a2*a4*v
x 3x x 3 x
df(v,t)=---------------------------------------------------------
a8
4 10 2 5 3
df(u,s)=(u *a8 *b23 + ----*u *f(v,v)*a2*a4*a8 *b23 + ---*u *a2*a8 *b23*u
5x 9 3x 3 3x
10 3 2
+ ----*u *u *a2*a8 *b23 + 5*u *f(v,v )*a2*a4*a8 *b23
3 2x x 2x x
25 2 50 2
+ ----*u *f(v ,v )*a2*a4*a8 *b23 + ----*u *f(v,v )*a2*a4*a8 *b23
6 x x x 9 x 2x
5 2 2 2 10 2
+ ----*u *f(v,v) *a2 *a4 *b23 + ----*u *f(v,v)*a2 *a4*a8*b23*u
81 x 9 x
5 2 2 2 25 3
+ ---*u *a2 *a8 *b23*u + ----*f(v ,v )*a4*a8 *b23
6 x 3 2x 3x
3 25 2
+ 5*f(v ,v )*a4*a8 *b23 + ----*f(v ,v )*f(v,v)*a2*a4 *a8*b23
x 4x 27 x 2x
50 2 10 2
+ ----*f(v ,v )*a2*a4*a8 *b23*u + ----*f(v ,v )*f(v,v )*a2*a4 *a8*b23
9 x 2x 9 x x x
5 3 10 2
+ ---*f(v,v )*a4*a8 *b23 + ----*f(v,v )*f(v,v)*a2*a4 *a8*b23
3 5x 27 3x
25 2 35 2
+ ----*f(v,v )*a2*a4*a8 *b23*u + ----*f(v,v )*f(v,v )*a2*a4 *a8*b23
9 3x 27 2x x
20 2 2 10 2 2
+ ----*f(v,v )*f(v,v)*a2 *a4 *b23*u + ----*f(v,v )*a2 *a4*a8*b23*u )/
81 x 9 x
4
a8
5 3 10 3 10 3
df(v,s)=(---*u *a2*a8 *b23*v + ----*u *v *a2*a8 *b23 + ----*u *v *a2*a8 *b23
3 3x 3 2x x 3 x 2x
10 2 5 2 2
+ ----*u *f(v,v)*a2 *a4*a8*b23*v + ---*u *a2 *a8 *b23*u*v
27 x 3 x
4 5 3 5 2
+ v *a8 *b23 + ---*v *a2*a8 *b23*u + ---*v *f(v,v )*a2*a4*a8 *b23
5x 3 3x 9 2x x
5 2 10 2
+ ---*v *f(v ,v )*a2*a4*a8 *b23 + ----*v *f(v,v )*a2*a4*a8 *b23
6 x x x 9 x 2x
5 2 5 2 2 2
+ ----*v *f(v,v)*a2 *a4*a8*b23*u + ---*v *a2 *a8 *b23*u
27 x 6 x
20 2 10 2
+ ----*f(v ,v )*a2*a4*a8 *b23*v + ----*f(v,v )*a2*a4*a8 *b23*v
9 x 2x 9 3x
5 2 2 25 2
+ ----*f(v,v )*f(v,v)*a2 *a4 *b23*v + ----*f(v,v )*a2 *a4*a8*b23*u*v)/
81 x 27 x
4
a8