Solution 20 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2
---*a18 *a4*b1
8
b42=----------------
2
a1 *a13
1 2 2 2
---*a1 *a18 *b1 + a13 *a18*a4*b1
4
b41=----------------------------------
3
a1 *a13
2 2
3*a13 *a4 *b1
b40=---------------
4
a1
b39=0
2 3
2*a1 *a13*a18*b1 + 2*a13 *a4*b1
b38=---------------------------------
4
a1
2 2
- a1 *a18*b1 + 8*a13 *a4*b1
b37=------------------------------
3
a1
b36=0
1 2 2
---*a1 *a18*b1 + 2*a13 *a4*b1
2
b35=-------------------------------
3
a1
a13*a4*b1
b34=-----------
2
a1
a13*a4*b1
b33=-----------
2
a1
b32=0
b31=0
3
4*a13 *b1
b30=-----------
3
a1
b29=0
2
6*a13 *b1
b28=-----------
2
a1
b27=0
b26=0
a13*b1
b25=--------
a1
b24=0
1 2 2
- ---*a18 *a4 *b1
8
b23=--------------------
3
a1 *a13
1 2 2 2 2
- ---*a1 *a18 *a4*b1 - a13 *a18*a4 *b1
4
b22=-----------------------------------------
4
a1 *a13
b21=0
2 3 2
- 2*a1 *a13*a18*a4*b1 - 2*a13 *a4 *b1
b20=----------------------------------------
5
a1
2 2 2
a1 *a18*a4*b1 + 4*a13 *a4 *b1
b19=-------------------------------
4
a1
1 2 2 2
- ---*a1 *a18*a4*b1 + a13 *a4 *b1
2
b18=------------------------------------
4
a1
2
6*a13*a4 *b1
b17=--------------
3
a1
2
2*a13*a4 *b1
b16=--------------
3
a1
2
2*a13*a4 *b1
b15=--------------
3
a1
3
- 4*a13 *a4*b1
b14=-----------------
4
a1
2
12*a13 *a4*b1
b13=---------------
3
a1
2
6*a13 *a4*b1
b12=--------------
3
a1
6*a13*a4*b1
b11=-------------
2
a1
6*a13*a4*b1
b10=-------------
2
a1
12*a13*a4*b1
b9=--------------
2
a1
2*a13*a4*b1
b8=-------------
2
a1
a4*b1
b7=-------
a1
3*a4*b1
b6=---------
a1
b5=0
2
12*a13 *b1
b4=------------
2
a1
6*a13*b1
b3=----------
a1
6*a13*b1
b2=----------
a1
1 2
---*a1*a18
8
a19=-------------
2
a13
1 2 2
- ---*a1 *a18 + 2*a13 *a4
2
a17=----------------------------
a1*a13
a16=0
2
2*a13
a15=--------
a1
a14=0
a12=0
1 2
- ---*a18 *a4
8
a11=----------------
2
a13
- a18*a4
a10=-----------
a1
1
---*a18*a4
2
a9=------------
a13
2
- 2*a13 *a4
a8=--------------
2
a1
4*a13*a4
a7=----------
a1
a13*a4
a6=--------
a1
a5=a4
a3=0
a2=4*a13
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,a4,a13,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 3 2 3
df(u,t)=(u *a1 *a13 + u *f(v,v)*a1*a13 *a4 + 4*u *a1 *a13 *u
2x x x
2 2 2 2
+ f(v ,v )*a1 *a13 *a4 + f(v,v )*a1 *a13 *a4
x x 2x
1 2 3
+ ---*f(v,v )*f(v,v)*a1 *a13*a18*a4 + 4*f(v,v )*a1*a13 *a4*u
2 x x
1 3 2 2 2 2
- ---*f(v,v) *a1 *a18 *a4 - f(v,v) *a1*a13 *a18*a4*u
8
4 2 2 2
- 2*f(v,v)*a13 *a4*u )/(a1 *a13 )
3 1 2 3
df(v,t)=(u *a1*a13 *v - ---*f(v,v )*a1 *a13*a18*v + 2*f(v,v )*a13 *a4*v
x 2 x x
1 2 2 2 2 4 2
+ ---*f(v,v) *a1 *a18 *v + f(v,v)*a1*a13 *a18*u*v + 2*a13 *u *v)/(a1
8
2
*a13 )
5 3 2 4 2
df(u,s)=(u *a1 *a13*b1 + 2*u *f(v,v)*a1 *a13 *a4*b1 + 6*u *a1 *a13 *b1*u
3x 2x 2x
2 4 2 3 2
+ 6*u *a1 *a13 *b1 + 12*u *f(v,v )*a1 *a13 *a4*b1
x x x
1 2 3 2 3 2
- ---*u *f(v,v) *a1 *a13*a18*a4*b1 + u *f(v,v) *a1*a13 *a4 *b1
2 x x
2 3 3 3 2
+ 6*u *f(v,v)*a1 *a13 *a4*b1*u + 12*u *a1 *a13 *b1*u
x x
4 2 2 2
+ 3*f(v ,v )*a1 *a13*a4*b1 + 2*f(v ,v )*f(v,v)*a1 *a13 *a4 *b1
x 2x x x
3 2 4
+ 6*f(v ,v )*a1 *a13 *a4*b1*u + f(v,v )*a1 *a13*a4*b1
x x 3x
2 2 2 3 2
+ 2*f(v,v )*f(v,v)*a1 *a13 *a4 *b1 + 6*f(v,v )*a1 *a13 *a4*b1*u
2x 2x
2 2 2 2 3
+ 6*f(v,v ) *a1 *a13 *a4 *b1 + f(v,v )*f(v,v)*a1 *a13*a18*a4*b1*u
x x
3 2 2 3 2
+ 4*f(v,v )*f(v,v)*a1*a13 *a4 *b1*u + 12*f(v,v )*a1 *a13 *a4*b1*u
x x
1 4 2 2 2 1 3 3 2
- ---*f(v,v) *a1 *a18 *a4 *b1 - ---*f(v,v) *a1 *a18 *a4*b1*u
8 4
3 2 2 2 2 2 2
- f(v,v) *a1*a13 *a18*a4 *b1*u - 2*f(v,v) *a1 *a13 *a18*a4*b1*u
2 4 2 2 4 3 5
- 2*f(v,v) *a13 *a4 *b1*u - 4*f(v,v)*a1*a13 *a4*b1*u )/(a1 *a13)
3 2 1 3
df(v,s)=(u *a1 *a13 *b1*v + ---*u *f(v,v)*a1 *a13*a18*b1*v
2x 2 x
3 2 3
+ 2*u *f(v,v)*a1*a13 *a4*b1*v + 6*u *a1 *a13 *b1*u*v
x x
2 2 2 2
+ f(v ,v )*a1 *a13 *a4*b1*v + f(v,v )*a1 *a13 *a4*b1*v
x x 2x
3 2 3
+ 3*f(v,v )*f(v,v)*a13 *a4 *b1*v - f(v,v )*a1 *a13*a18*b1*u*v
x x
3 1 3 2 2
+ 8*f(v,v )*a1*a13 *a4*b1*u*v + ---*f(v,v) *a1 *a18 *a4*b1*v
x 8
1 2 3 2 2 2
+ ---*f(v,v) *a1 *a18 *b1*u*v + f(v,v) *a1*a13 *a18*a4*b1*u*v
4
2 2 2 4 2
+ 2*f(v,v)*a1 *a13 *a18*b1*u *v + 2*f(v,v)*a13 *a4*b1*u *v
4 3 4
+ 4*a1*a13 *b1*u *v)/(a1 *a13)