Solution 5 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
35 2
----*a6 *b23
36
b40=--------------
2
a8
35 2
-----*a6 *b23
288
b39=---------------
2
a8
20
----*a2*a6*b23
9
b38=----------------
2
a8
25
----*a2*a6*b23
36
b37=----------------
2
a8
35
----*a2*a6*b23
36
b36=----------------
2
a8
5
---*a6*b23
2
b35=------------
a8
35
----*a6*b23
6
b34=-------------
a8
10
----*a6*b23
3
b33=-------------
a8
35
----*a6*b23
12
b32=-------------
a8
5
---*a6*b23
2
b31=------------
a8
5
----*a6*b23
12
b30=-------------
a8
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
35 2
----*a6 *b23
36
b21=--------------
2
a8
35 2
-----*a6 *b23
288
b20=---------------
2
a8
35 2
----*a6 *b23
4
b19=--------------
a2*a8
35 2
----*a6 *b23
24
b18=--------------
a2*a8
35 2
----*a6 *b23
4
b17=--------------
a2*a8
35 2
----*a6 *b23
8
b16=--------------
a2*a8
5
---*a2*a6*b23
3
b15=---------------
2
a8
5
---*a2*a6*b23
4
b14=---------------
2
a8
25
----*a6*b23
6
b13=-------------
a8
65
----*a6*b23
6
b12=-------------
a8
25
----*a6*b23
3
b11=-------------
a8
95
----*a6*b23
12
b10=-------------
a8
15
----*a6*b23
2
b9=-------------
a8
5
---*a6*b23
4
b8=------------
a8
5
---*a6*b23
2
b7=------------
a2
10*a6*b23
b6=-----------
a2
35
----*a6*b23
2
b5=-------------
a2
5 2
---*a2 *b23
6
b4=-------------
2
a8
10
----*a2*b23
3
b3=-------------
a8
5
---*a2*b23
3
b2=------------
a8
b1=b23
a12=a6
1
a11=---*a6
4
a10=a2
a9=a2
a7=0
a6=a6
1
a5=---*a6
4
3
---*a6*a8
2
a4=-----------
a2
9
---*a6*a8
2
a3=-----------
a2
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,a2,a6,a8
Relevance for the application:
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1 2 9
df(u,t)=(u *a2*a8 + ---*u *f(v,v)*a2*a6 + u *a2 *u + ---*f(v ,v )*a6*a8
3x 4 x x 2 x 2x
3
+ ---*f(v,v )*a6*a8 + f(v,v )*a2*a6*u)/a2
2 3x x
1
df(v,t)=u *a2*v + v *a8 + ---*v *f(v,v)*a6 + v *a2*u + f(v,v )*a6*v
x 3x 4 x x x
2 5 5 2
df(u,s)=(u *a2*a8 *b23 + ---*u *f(v,v)*a2*a6*a8*b23 + ---*u *a2 *a8*b23*u
5x 4 3x 3 3x
10 2 15
+ ----*u *u *a2 *a8*b23 + ----*u *f(v,v )*a2*a6*a8*b23
3 2x x 2 2x x
95 25
+ ----*u *f(v ,v )*a2*a6*a8*b23 + ----*u *f(v,v )*a2*a6*a8*b23
12 x x x 3 x 2x
35 2 2 5 2
+ -----*u *f(v,v) *a2*a6 *b23 + ---*u *f(v,v)*a2 *a6*b23*u
288 x 4 x
5 3 2 35 2
+ ---*u *a2 *b23*u + ----*f(v ,v )*a6*a8 *b23
6 x 2 2x 3x
2 35 2
+ 10*f(v ,v )*a6*a8 *b23 + ----*f(v ,v )*f(v,v)*a6 *a8*b23
x 4x 8 x 2x
65 35 2
+ ----*f(v ,v )*a2*a6*a8*b23*u + ----*f(v ,v )*f(v,v )*a6 *a8*b23
6 x 2x 4 x x x
5 2 35 2
+ ---*f(v,v )*a6*a8 *b23 + ----*f(v,v )*f(v,v)*a6 *a8*b23
2 5x 24 3x
25 35 2
+ ----*f(v,v )*a2*a6*a8*b23*u + ----*f(v,v )*f(v,v )*a6 *a8*b23
6 3x 4 2x x
35 2 5 2 2
+ ----*f(v,v )*f(v,v)*a2*a6 *b23*u + ---*f(v,v )*a2 *a6*b23*u )/(a2
36 x 3 x
2
*a8 )
5 10 10
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
35 5 2 2
+ ----*u *f(v,v)*a2*a6*b23*v + ---*u *a2 *b23*u*v + v *a8 *b23
36 x 3 x 5x
5 5
+ ----*v *f(v,v)*a6*a8*b23 + ---*v *a2*a8*b23*u
12 3x 3 3x
5 35
+ ---*v *f(v,v )*a6*a8*b23 + ----*v *f(v ,v )*a6*a8*b23
2 2x x 12 x x x
10 35 2 2
+ ----*v *f(v,v )*a6*a8*b23 + -----*v *f(v,v) *a6 *b23
3 x 2x 288 x
25 5 2 2
+ ----*v *f(v,v)*a2*a6*b23*u + ---*v *a2 *b23*u
36 x 6 x
35 5
+ ----*f(v ,v )*a6*a8*b23*v + ---*f(v,v )*a6*a8*b23*v
6 x 2x 2 3x
35 2 20 2
+ ----*f(v,v )*f(v,v)*a6 *b23*v + ----*f(v,v )*a2*a6*b23*u*v)/a8
36 x 9 x