Solution 8 to problem l21o35
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b40=0
5 2
---*a11 *b23
9
b39=--------------
2
a8
5
---*a11*a2*b23
6
b38=----------------
2
a8
5
---*a11*a2*b23
6
b37=----------------
2
a8
5
---*a11*a2*b23
9
b36=----------------
2
a8
b35=0
5*a11*b23
b34=-----------
a8
10
----*a11*b23
3
b33=--------------
a8
5*a11*b23
b32=-----------
a8
5*a11*b23
b31=-----------
a8
5
---*a11*b23
3
b30=-------------
a8
5 2
----*a2 *b23
18
b29=--------------
2
a8
5 2
---*a2 *b23
9
b28=-------------
2
a8
5
---*a2*b23
6
b27=------------
a8
5
---*a2*b23
3
b26=------------
a8
5
---*a2*b23
3
b25=------------
a8
5
---*a2*b23
6
b24=------------
a8
80 3
- ----*a11 *b23
9
b22=------------------
2
a2*a8
80 2
- ----*a11 *b23
9
b21=------------------
2
a8
25 2
- ----*a11 *b23
9
b20=------------------
2
a8
2
- 80*a11 *b23
b19=----------------
a2*a8
2
- 20*a11 *b23
b18=----------------
a2*a8
2
- 40*a11 *b23
b17=----------------
a2*a8
100 2
- -----*a11 *b23
3
b16=-------------------
a2*a8
b15=0
10
- ----*a11*a2*b23
9
b14=--------------------
2
a8
20
- ----*a11*b23
3
b13=-----------------
a8
20
----*a11*b23
3
b12=--------------
a8
- 10*a11*b23
b11=---------------
a8
5*a11*b23
b10=-----------
a8
20
- ----*a11*b23
3
b9=-----------------
a8
10
- ----*a11*b23
3
b8=-----------------
a8
- 10*a11*b23
b7=---------------
a2
b6=0
10*a11*b23
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=a11
1
a10=---*a2
2
1
a9=---*a2
2
2
- 8*a11
a7=-----------
a2
a6=0
a5= - a11
- 6*a11*a8
a4=-------------
a2
6*a11*a8
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,a11,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=(u *a2*a8 - u *f(v,v)*a11*a2 + u *a2 *u + 6*f(v ,v )*a11*a8
3x x x x 2x
2
- 6*f(v,v )*a11*a8 - 8*f(v,v )*f(v,v)*a11 )/a2
3x x
1 1
df(v,t)=---*u *a2*v + v *a8 + v *f(v,v)*a11 + ---*v *a2*u + f(v,v )*a11*v
2 x 3x x 2 x x
2 10 5 2
df(u,s)=(u *a2*a8 *b23 - ----*u *f(v,v)*a11*a2*a8*b23 + ---*u *a2 *a8*b23*u
5x 3 3x 3 3x
10 2 20
+ ----*u *u *a2 *a8*b23 - ----*u *f(v,v )*a11*a2*a8*b23
3 2x x 3 2x x
+ 5*u *f(v ,v )*a11*a2*a8*b23 - 10*u *f(v,v )*a11*a2*a8*b23
x x x x 2x
25 2 2 10 2
- ----*u *f(v,v) *a11 *a2*b23 - ----*u *f(v,v)*a11*a2 *b23*u
9 x 9 x
5 3 2 2
+ ---*u *a2 *b23*u + 10*f(v ,v )*a11*a8 *b23
6 x 2x 3x
100 2 20
- -----*f(v ,v )*f(v,v)*a11 *a8*b23 + ----*f(v ,v )*a11*a2*a8*b23*u
3 x 2x 3 x 2x
2 2
- 40*f(v ,v )*f(v,v )*a11 *a8*b23 - 10*f(v,v )*a11*a8 *b23
x x x 5x
2 20
- 20*f(v,v )*f(v,v)*a11 *a8*b23 - ----*f(v,v )*a11*a2*a8*b23*u
3x 3 3x
2 80 2 3
- 80*f(v,v )*f(v,v )*a11 *a8*b23 - ----*f(v,v )*f(v,v) *a11 *b23
2x x 9 x
80 2 2
- ----*f(v,v )*f(v,v)*a11 *a2*b23*u)/(a2*a8 )
9 x
5 5 5
df(v,s)=(---*u *a2*a8*b23*v + ---*u *v *a2*a8*b23 + ---*u *v *a2*a8*b23
6 3x 3 2x x 3 x 2x
5 5 2 2
+ ---*u *f(v,v)*a11*a2*b23*v + ---*u *a2 *b23*u*v + v *a8 *b23
9 x 9 x 5x
5 5
+ ---*v *f(v,v)*a11*a8*b23 + ---*v *a2*a8*b23*u
3 3x 6 3x
+ 5*v *f(v,v )*a11*a8*b23 + 5*v *f(v ,v )*a11*a8*b23
2x x x x x
10 5 2 2
+ ----*v *f(v,v )*a11*a8*b23 + ---*v *f(v,v) *a11 *b23
3 x 2x 9 x
5 5 2 2
+ ---*v *f(v,v)*a11*a2*b23*u + ----*v *a2 *b23*u
6 x 18 x
5 2
+ 5*f(v ,v )*a11*a8*b23*v + ---*f(v,v )*a11*a2*b23*u*v)/a8
x 2x 6 x