Solution 14 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
b40= - b39
6*a11*a9*b1
b38=-------------
2
a1
- 12*a11*a9*b1
b37=-----------------
2
a1
3*a11*a9*b1
b36=-------------
2
a1
1
- ---*a11*b1
2
b35=---------------
a1
3
- ---*a11*b1
2
b34=---------------
a1
2*a11*b1
b33=----------
a1
2*a11*b1
b32=----------
a1
b31=0
b30=0
2
24*a9 *b1
b29=-----------
2
a1
2
- 12*a9 *b1
b28=--------------
2
a1
b27=0
b26=0
- 4*a9*b1
b25=------------
a1
a9*b1
b24=-------
a1
b23=0
15 3
- ----*a11 *b1
4
b22=-----------------
2
a1 *a9
2
27*a11 *b1
b21=------------
2
a1
2
9*a11 *b1
b20=-----------
2
a1
2
- 9*a11 *b1
b19=--------------
a1*a9
11 2
- ----*a11 *b1
4
b18=-----------------
a1*a9
2
- 9*a11 *b1
b17=--------------
a1*a9
33 2
- ----*a11 *b1
4
b16=-----------------
a1*a9
- 48*a11*a9*b1
b15=-----------------
2
a1
- 66*a11*a9*b1
b14=-----------------
2
a1
10*a11*b1
b13=-----------
a1
30*a11*b1
b12=-----------
a1
20*a11*b1
b11=-----------
a1
20*a11*b1
b10=-----------
a1
18*a11*b1
b9=-----------
a1
11
----*a11*b1
2
b8=-------------
a1
1
- ---*a11*b1
2
b7=---------------
a9
5
- ---*a11*b1
2
b6=---------------
a9
- 5*a11*b1
b5=-------------
a9
2
120*a9 *b1
b4=------------
2
a1
- 40*a9*b1
b3=-------------
a1
- 20*a9*b1
b2=-------------
a1
1
a12= - ---*a11
2
a10= - 4*a9
a8=0
5 2
- ---*a11
4
a7=-------------
a9
a6=4*a11
7
a5=---*a11
2
1
- ---*a1*a11
2
a4=---------------
a9
3
- ---*a1*a11
2
a3=---------------
a9
a2= - 12*a9
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:
b39,b1,a11,a9,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
7 2 3
df(u,t)=(u *a1*a9 + ---*u *f(v,v)*a11*a9 - 12*u *a9 *u - ---*f(v ,v )*a1*a11
3x 2 x x 2 x 2x
1 5 2
- ---*f(v,v )*a1*a11 - ---*f(v,v )*f(v,v)*a11 + 4*f(v,v )*a11*a9*u)/
2 3x 4 x x
a9
1
df(v,t)=u *a9*v + v *f(v,v)*a11 - 4*v *a9*u - ---*f(v,v )*a11*v
x x x 2 x
2 11 2
df(u,s)=(u *a1 *a9*b1 + ----*u *f(v,v)*a1*a11*a9*b1 - 20*u *a1*a9 *b1*u
5x 2 3x 3x
2
- 40*u *u *a1*a9 *b1 + 18*u *f(v,v )*a1*a11*a9*b1
2x x 2x x
+ 20*u *f(v ,v )*a1*a11*a9*b1 + 20*u *f(v,v )*a1*a11*a9*b1
x x x x 2x
2 2 2
+ 9*u *f(v,v) *a11 *a9*b1 - 66*u *f(v,v)*a11*a9 *b1*u
x x
3 2 2
+ 120*u *a9 *b1*u - 5*f(v ,v )*a1 *a11*b1
x 2x 3x
5 2 33 2
- ---*f(v ,v )*a1 *a11*b1 - ----*f(v ,v )*f(v,v)*a1*a11 *b1
2 x 4x 4 x 2x
2
+ 30*f(v ,v )*a1*a11*a9*b1*u - 9*f(v ,v )*f(v,v )*a1*a11 *b1
x 2x x x x
1 2 11 2
- ---*f(v,v )*a1 *a11*b1 - ----*f(v,v )*f(v,v)*a1*a11 *b1
2 5x 4 3x
2
+ 10*f(v,v )*a1*a11*a9*b1*u - 9*f(v,v )*f(v,v )*a1*a11 *b1
3x 2x x
15 2 3 2
- ----*f(v,v )*f(v,v) *a11 *b1 + 27*f(v,v )*f(v,v)*a11 *a9*b1*u
4 x x
2 2 2
- 48*f(v,v )*a11*a9 *b1*u )/(a1 *a9)
x
df(v,s)=(u *a1*a9*b1*v - 4*u *v *a1*a9*b1 + 3*u *f(v,v)*a11*a9*b1*v
3x 2x x x
2
- 12*u *a9 *b1*u*v + 2*v *f(v ,v )*a1*a11*b1 + 2*v *f(v,v )*a1*a11*b1
x x x x x 2x
2 2 2 2
+ v *f(v,v) *a1 *b39 - 12*v *f(v,v)*a11*a9*b1*u + 24*v *a9 *b1*u
x x x
3 1
- ---*f(v ,v )*a1*a11*b1*v - ---*f(v,v )*a1*a11*b1*v
2 x 2x 2 3x
2 2
- f(v,v )*f(v,v)*a1 *b39*v + 6*f(v,v )*a11*a9*b1*u*v)/a1
x x