Solution 17 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
1 2 2
- -----*a2 *a3 *b1
108
b40=---------------------
4
a1
1 2 2
-----*a2 *a3 *b1
216
b39=------------------
4
a1
1 2
- ----*a2 *a3*b1
18
b38=-------------------
3
a1
1 2
----*a2 *a3*b1
18
b37=----------------
3
a1
1 2
- ----*a2 *a3*b1
36
b36=-------------------
3
a1
1
- ----*a2*a3*b1
18
b35=------------------
2
a1
1
- ---*a2*a3*b1
6
b34=-----------------
2
a1
1
---*a2*a3*b1
9
b33=--------------
2
a1
1
---*a2*a3*b1
9
b32=--------------
2
a1
b31=0
b30=0
1 2
---*a2 *b1
6
b29=------------
2
a1
1 2
- ---*a2 *b1
6
b28=---------------
2
a1
b27=0
b26=0
1
---*a2*b1
3
b25=-----------
a1
1
- ---*a2*b1
6
b24=--------------
a1
b23=0
1 2 3
-----*a2 *a3 *b1
108
b22=------------------
5
a1
5 2 2
----*a2 *a3 *b1
54
b21=-----------------
4
a1
7 2 2
-----*a2 *a3 *b1
216
b20=------------------
4
a1
1 2
---*a2*a3 *b1
3
b19=---------------
3
a1
1 2
---*a2*a3 *b1
9
b18=---------------
3
a1
1 2
---*a2*a3 *b1
3
b17=---------------
3
a1
1 2
---*a2*a3 *b1
3
b16=---------------
3
a1
2 2
---*a2 *a3*b1
9
b15=---------------
3
a1
1 2
---*a2 *a3*b1
3
b14=---------------
3
a1
5
---*a2*a3*b1
9
b13=--------------
2
a1
5
---*a2*a3*b1
3
b12=--------------
2
a1
10
----*a2*a3*b1
9
b11=---------------
2
a1
10
----*a2*a3*b1
9
b10=---------------
2
a1
a2*a3*b1
b9=----------
2
a1
1
---*a2*a3*b1
3
b8=--------------
2
a1
1
---*a3*b1
3
b7=-----------
a1
5
---*a3*b1
3
b6=-----------
a1
10
----*a3*b1
3
b5=------------
a1
5 2
---*a2 *b1
6
b4=------------
2
a1
10
----*a2*b1
3
b3=------------
a1
5
---*a2*b1
3
b2=-----------
a1
a12= - a11
1
a10=---*a2
3
1
a9= - ---*a2
6
a8=0
1 2
----*a2*a3
18
a7=-------------
2
a1
2
---*a2*a3
9
a6=-----------
a1
2
---*a2*a3
9
a5=-----------
a1
1
a4=---*a3
3
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:
b1,a11,a2,a3,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 2 2
df(u,t)=(u *a1 + ---*u *f(v,v)*a1*a2*a3 + u *a1 *a2*u + f(v ,v )*a1 *a3
3x 9 x x x 2x
1 2 1 2
+ ---*f(v,v )*a1 *a3 + ----*f(v,v )*f(v,v)*a2*a3
3 3x 18 x
2 2
+ ---*f(v,v )*a1*a2*a3*u)/a1
9 x
1 1
df(v,t)= - ---*u *a2*v + v *f(v,v)*a11 + ---*v *a2*u - f(v,v )*a11*v
6 x x 3 x x
5 1 3 5 4
df(u,s)=(u *a1 *b1 + ---*u *f(v,v)*a1 *a2*a3*b1 + ---*u *a1 *a2*b1*u
5x 3 3x 3 3x
10 4 3
+ ----*u *u *a1 *a2*b1 + u *f(v,v )*a1 *a2*a3*b1
3 2x x 2x x
10 3 10 3
+ ----*u *f(v ,v )*a1 *a2*a3*b1 + ----*u *f(v,v )*a1 *a2*a3*b1
9 x x x 9 x 2x
7 2 2 2 1 2 2
+ -----*u *f(v,v) *a1*a2 *a3 *b1 + ---*u *f(v,v)*a1 *a2 *a3*b1*u
216 x 3 x
5 3 2 2 10 4
+ ---*u *a1 *a2 *b1*u + ----*f(v ,v )*a1 *a3*b1
6 x 3 2x 3x
5 4 1 2 2
+ ---*f(v ,v )*a1 *a3*b1 + ---*f(v ,v )*f(v,v)*a1 *a2*a3 *b1
3 x 4x 3 x 2x
5 3 1 2 2
+ ---*f(v ,v )*a1 *a2*a3*b1*u + ---*f(v ,v )*f(v,v )*a1 *a2*a3 *b1
3 x 2x 3 x x x
1 4 1 2 2
+ ---*f(v,v )*a1 *a3*b1 + ---*f(v,v )*f(v,v)*a1 *a2*a3 *b1
3 5x 9 3x
5 3 1 2 2
+ ---*f(v,v )*a1 *a2*a3*b1*u + ---*f(v,v )*f(v,v )*a1 *a2*a3 *b1
9 3x 3 2x x
1 2 2 3
+ -----*f(v,v )*f(v,v) *a2 *a3 *b1
108 x
5 2 2 2 2 2 2
+ ----*f(v,v )*f(v,v)*a1*a2 *a3 *b1*u + ---*f(v,v )*a1 *a2 *a3*b1*u )/
54 x 9 x
5
a1
1 3 1 3
df(v,s)=( - ---*u *a1 *a2*b1*v + ---*u *v *a1 *a2*b1
6 3x 3 2x x
1 2 1 2 2
- ----*u *f(v,v)*a1*a2 *a3*b1*v - ---*u *a1 *a2 *b1*u*v
36 x 6 x
1 2 1 2
+ ---*v *f(v ,v )*a1 *a2*a3*b1 + ---*v *f(v,v )*a1 *a2*a3*b1
9 x x x 9 x 2x
1 2 2 2 1 2
+ -----*v *f(v,v) *a2 *a3 *b1 + ----*v *f(v,v)*a1*a2 *a3*b1*u
216 x 18 x
1 2 2 2 1 2
+ ---*v *a1 *a2 *b1*u - ---*f(v ,v )*a1 *a2*a3*b1*v
6 x 6 x 2x
1 2 1 2 2
- ----*f(v,v )*a1 *a2*a3*b1*v - -----*f(v,v )*f(v,v)*a2 *a3 *b1*v
18 3x 108 x
1 2 4
- ----*f(v,v )*a1*a2 *a3*b1*u*v)/a1
18 x