Solution 11 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40=0
5 2
-----*a6 *b23
288
b39=---------------
2
a8
b38=0
5
- ----*a10*a6*b23
36
b37=--------------------
2
a8
b36=0
b35=0
b34=0
5
- ----*a6*b23
12
b33=----------------
a8
5
- ----*a6*b23
12
b32=----------------
a8
5
- ---*a6*b23
6
b31=---------------
a8
5
- ----*a6*b23
12
b30=----------------
a8
5 2
----*a10 *b23
18
b29=---------------
2
a8
b28=0
5
---*a10*b23
3
b27=-------------
a8
5
---*a10*b23
3
b26=-------------
a8
5
---*a10*b23
6
b25=-------------
a8
b24=0
5 3
-----*a6 *b23
144
b22=---------------
2
a10*a8
5 2
- ----*a6 *b23
18
b21=-----------------
2
a8
5 2
- ----*a6 *b23
96
b20=-----------------
2
a8
25 2
- ----*a6 *b23
24
b19=-----------------
a10*a8
5 2
- ----*a6 *b23
16
b18=-----------------
a10*a8
5 2
- ---*a6 *b23
8
b17=----------------
a10*a8
5 2
- ----*a6 *b23
16
b16=-----------------
a10*a8
5
---*a10*a6*b23
9
b15=----------------
2
a8
5
----*a10*a6*b23
12
b14=-----------------
2
a8
5
---*a6*b23
4
b13=------------
a8
5
---*a6*b23
4
b12=------------
a8
5
---*a6*b23
3
b11=------------
a8
5
---*a6*b23
6
b10=------------
a8
5
---*a6*b23
4
b9=------------
a8
5
----*a6*b23
24
b8=-------------
a8
5
---*a6*b23
8
b7=------------
a10
5
---*a6*b23
8
b6=------------
a10
5
---*a6*b23
4
b5=------------
a10
5 2
- ---*a10 *b23
6
b4=-----------------
2
a8
5
- ---*a10*b23
3
b3=----------------
a8
5
- ---*a10*b23
6
b2=----------------
a8
1
b1= - ---*b23
4
a12=0
1
a11= - ---*a6
4
a9=0
1 2
- ---*a6
4
a7=------------
a10
a6=a6
1
a5=---*a6
4
3
---*a6*a8
4
a4=-----------
a10
3
---*a6*a8
4
a3=-----------
a10
a2= - a10
1
a1= - ---*a8
2
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,a6,a10,a8
Relevance for the application:
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1 1 2
df(u,t)=( - ---*u *a10*a8 + ---*u *f(v,v)*a10*a6 - u *a10 *u
2 3x 4 x x
3 3 1 2
+ ---*f(v ,v )*a6*a8 + ---*f(v,v )*a6*a8 - ---*f(v,v )*f(v,v)*a6
4 x 2x 4 3x 4 x
+ f(v,v )*a10*a6*u)/a10
x
1
df(v,t)=v *a8 - ---*v *f(v,v)*a6 + v *a10*u
3x 4 x x
1 2 5
df(u,s)=( - ---*u *a10*a8 *b23 + ----*u *f(v,v)*a10*a6*a8*b23
4 5x 24 3x
5 2 5 2
- ---*u *a10 *a8*b23*u - ---*u *u *a10 *a8*b23
6 3x 3 2x x
5 5
+ ---*u *f(v,v )*a10*a6*a8*b23 + ---*u *f(v ,v )*a10*a6*a8*b23
4 2x x 6 x x x
5 5 2 2
+ ---*u *f(v,v )*a10*a6*a8*b23 - ----*u *f(v,v) *a10*a6 *b23
3 x 2x 96 x
5 2 5 3 2
+ ----*u *f(v,v)*a10 *a6*b23*u - ---*u *a10 *b23*u
12 x 6 x
5 2 5 2
+ ---*f(v ,v )*a6*a8 *b23 + ---*f(v ,v )*a6*a8 *b23
4 2x 3x 8 x 4x
5 2 5
- ----*f(v ,v )*f(v,v)*a6 *a8*b23 + ---*f(v ,v )*a10*a6*a8*b23*u
16 x 2x 4 x 2x
5 2 5 2
- ---*f(v ,v )*f(v,v )*a6 *a8*b23 + ---*f(v,v )*a6*a8 *b23
8 x x x 8 5x
5 2 5
- ----*f(v,v )*f(v,v)*a6 *a8*b23 + ---*f(v,v )*a10*a6*a8*b23*u
16 3x 4 3x
25 2 5 2 3
- ----*f(v,v )*f(v,v )*a6 *a8*b23 + -----*f(v,v )*f(v,v) *a6 *b23
24 2x x 144 x
5 2 5 2 2
- ----*f(v,v )*f(v,v)*a10*a6 *b23*u + ---*f(v,v )*a10 *a6*b23*u )/(a10
18 x 9 x
2
*a8 )
5 5 2
df(v,s)=(---*u *v *a10*a8*b23 + ---*u *v *a10*a8*b23 + v *a8 *b23
6 2x x 3 x 2x 5x
5 5
- ----*v *f(v,v)*a6*a8*b23 + ---*v *a10*a8*b23*u
12 3x 3 3x
5 5
- ---*v *f(v,v )*a6*a8*b23 - ----*v *f(v ,v )*a6*a8*b23
6 2x x 12 x x x
5 5 2 2
- ----*v *f(v,v )*a6*a8*b23 + -----*v *f(v,v) *a6 *b23
12 x 2x 288 x
5 5 2 2 2
- ----*v *f(v,v)*a10*a6*b23*u + ----*v *a10 *b23*u )/a8
36 x 18 x