Solution 12 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
5 2
---*a5 *b23
6
b39=-------------
2
a8
b38=0
5
---*a10*a5*b23
3
b37=----------------
2
a8
b36=0
b35=0
b34=0
10
----*a5*b23
3
b33=-------------
a8
5 5
----*a10*a3*b23 + ---*a5*a8*b23
18 3
b32=---------------------------------
2
a8
10
----*a5*b23
3
b31=-------------
a8
5
---*a5*b23
3
b30=------------
a8
5 2
---*a10 *b23
6
b29=--------------
2
a8
b28=0
5
---*a10*b23
3
b27=-------------
a8
5
---*a10*b23
3
b26=-------------
a8
5
---*a10*b23
3
b25=-------------
a8
b24=0
b22=0
b21=0
5 2
---*a5 *b23
6
b20=-------------
2
a8
b19=0
b18=0
10
----*a3*a5*b23
9
b17=----------------
2
a8
5
---*a3*a5*b23
3
b16=---------------
2
a8
b15=0
5
---*a10*a5*b23
3
b14=----------------
2
a8
b13=0
5
---*a10*a3*b23
3
b12=----------------
2
a8
10
----*a5*b23
3
b11=-------------
a8
5 5
---*a10*a3*b23 + ---*a5*a8*b23
6 3
b10=--------------------------------
2
a8
10
----*a5*b23
3
b9=-------------
a8
5
---*a5*b23
3
b8=------------
a8
b7=0
5
---*a3*b23
3
b6=------------
a8
10
----*a3*b23
3
b5=-------------
a8
5 2
---*a10 *b23
6
b4=--------------
2
a8
10
----*a10*b23
3
b3=--------------
a8
5
---*a10*b23
3
b2=-------------
a8
b1=b23
a12=0
a11=a5
a9=0
a7=0
a6=0
a4=0
a2=a10
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,a3,a5,a10,a8
Relevance for the application:
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df(u,t)=u *a8 + u *f(v,v)*a5 + u *a10*u + f(v ,v )*a3
3x x x x 2x
df(v,t)=v *a8 + v *f(v,v)*a5 + v *a10*u
3x x x
2 5 5
df(u,s)=(u *a8 *b23 + ---*u *f(v,v)*a5*a8*b23 + ---*u *a10*a8*b23*u
5x 3 3x 3 3x
10 10
+ ----*u *u *a10*a8*b23 + ----*u *f(v,v )*a5*a8*b23
3 2x x 3 2x x
5 5
+ ---*u *f(v ,v )*a10*a3*b23 + ---*u *f(v ,v )*a5*a8*b23
6 x x x 3 x x x
10 5 2 2
+ ----*u *f(v,v )*a5*a8*b23 + ---*u *f(v,v) *a5 *b23
3 x 2x 6 x
5 5 2 2
+ ---*u *f(v,v)*a10*a5*b23*u + ---*u *a10 *b23*u
3 x 6 x
10 5
+ ----*f(v ,v )*a3*a8*b23 + ---*f(v ,v )*a3*a8*b23
3 2x 3x 3 x 4x
5 5
+ ---*f(v ,v )*f(v,v)*a3*a5*b23 + ---*f(v ,v )*a10*a3*b23*u
3 x 2x 3 x 2x
10 2
+ ----*f(v ,v )*f(v,v )*a3*a5*b23)/a8
9 x x x
5 5 2
df(v,s)=(---*u *v *a10*a8*b23 + ---*u *v *a10*a8*b23 + v *a8 *b23
3 2x x 3 x 2x 5x
5 5
+ ---*v *f(v,v)*a5*a8*b23 + ---*v *a10*a8*b23*u
3 3x 3 3x
10 5
+ ----*v *f(v,v )*a5*a8*b23 + ----*v *f(v ,v )*a10*a3*b23
3 2x x 18 x x x
5 10
+ ---*v *f(v ,v )*a5*a8*b23 + ----*v *f(v,v )*a5*a8*b23
3 x x x 3 x 2x
5 2 2 5
+ ---*v *f(v,v) *a5 *b23 + ---*v *f(v,v)*a10*a5*b23*u
6 x 3 x
5 2 2 2
+ ---*v *a10 *b23*u )/a8
6 x