Solution 16 to problem l112o23
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
1 2 2 1 3 3
---*a1 *a13*a18*a4 *b1 - ---*a13 *a4 *b1
2 2
b42=------------------------------------------
6
a1
2 3 2
2*a1 *a13*a18*a4*b1 - a13 *a4 *b1
b41=-----------------------------------
5
a1
2 2 2
2*a1 *a18*a4*b1 - a13 *a4 *b1
b40=-------------------------------
4
a1
2 2 2
- a1 *a18*a4*b1 + 2*a13 *a4 *b1
b39=----------------------------------
4
a1
2 3
2*a1 *a13*a18*b1 + 2*a13 *a4*b1
b38=---------------------------------
4
a1
2 2
2*a1 *a18*b1 + 2*a13 *a4*b1
b37=-----------------------------
3
a1
2 2
- 2*a1 *a18*b1 + 4*a13 *a4*b1
b36=--------------------------------
3
a1
2 2
a1 *a18*b1 + a13 *a4*b1
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 3 1 3 4
- ---*a1 *a13*a18*a4 *b1 + ---*a13 *a4 *b1
2 2
b23=---------------------------------------------
7
a1
2 2 3 3
- 2*a1 *a13*a18*a4 *b1 + a13 *a4 *b1
b22=---------------------------------------
6
a1
2 2 2 3
- a1 *a18*a4 *b1 + 2*a13 *a4 *b1
b21=-----------------------------------
5
a1
2 3 2
- 2*a1 *a13*a18*a4*b1 - 2*a13 *a4 *b1
b20=----------------------------------------
5
a1
2 2
6*a13 *a4 *b1
b19=---------------
4
a1
2 2 2
- a1 *a18*a4*b1 + 2*a13 *a4 *b1
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 1 2 2
---*a1 *a18*a4 - ---*a13 *a4
2 2
a19=-------------------------------
3
a1
2 2
a1 *a18 - a13 *a4
a17=-------------------
a1*a13
2 2
- a1 *a18 + 2*a13 *a4
a16=------------------------
a1*a13
2
2*a13
a15=--------
a1
a14=0
a12=0
1 2 2 1 2 3
- ---*a1 *a18*a4 + ---*a13 *a4
2 2
a11=-----------------------------------
4
a1
- a18*a4
a10=-----------
a1
2
a13*a4
a9=---------
2
a1
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:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
5 3 4 4
df(u,t)=(u *a1 + u *f(v,v)*a1 *a13*a4 + 4*u *a1 *a13*u + f(v ,v )*a1 *a4
2x x x x x
4 2 2
+ f(v,v )*a1 *a4 + f(v,v )*f(v,v)*a1 *a13*a4
2x x
3 1 3 2 2
+ 4*f(v,v )*a1 *a13*a4*u - ---*f(v,v) *a1 *a18*a4
x 2
1 3 2 3 2 3
+ ---*f(v,v) *a13 *a4 - f(v,v) *a1 *a18*a4*u
2
2 2 2 4
- 2*f(v,v)*a1 *a13 *a4*u )/a1
3 2 4 2 2
df(v,t)=(u *a1 *a13 *v - v *f(v,v)*a1 *a18 + 2*v *f(v,v)*a1 *a13 *a4
x x x
4 2 2
+ f(v,v )*a1 *a18*v - f(v,v )*a1 *a13 *a4*v
x x
1 2 2 1 2 3 2
+ ---*f(v,v) *a1 *a13*a18*a4*v - ---*f(v,v) *a13 *a4 *v
2 2
3 2 3 2 3
+ f(v,v)*a1 *a13*a18*u*v + 2*a1 *a13 *u *v)/(a1 *a13)
7 5 6
df(u,s)=(u *a1 *b1 + 2*u *f(v,v)*a1 *a13*a4*b1 + 6*u *a1 *a13*b1*u
3x 2x 2x
2 6 5
+ 6*u *a1 *a13*b1 + 12*u *f(v,v )*a1 *a13*a4*b1
x x x
2 5 2 3 2 2
- u *f(v,v) *a1 *a18*a4*b1 + 2*u *f(v,v) *a1 *a13 *a4 *b1
x x
4 2 5 2 2
+ 6*u *f(v,v)*a1 *a13 *a4*b1*u + 12*u *a1 *a13 *b1*u
x x
6 4 2
+ 3*f(v ,v )*a1 *a4*b1 + 2*f(v ,v )*f(v,v)*a1 *a13*a4 *b1
x 2x x x
5 6
+ 6*f(v ,v )*a1 *a13*a4*b1*u + f(v,v )*a1 *a4*b1
x x 3x
4 2 5
+ 2*f(v,v )*f(v,v)*a1 *a13*a4 *b1 + 6*f(v,v )*a1 *a13*a4*b1*u
2x 2x
2 4 2 2 4 2
+ 6*f(v,v ) *a1 *a13*a4 *b1 - f(v,v )*f(v,v) *a1 *a18*a4 *b1
x x
2 2 2 3
+ 2*f(v,v )*f(v,v) *a1 *a13 *a4 *b1
x
3 2 2 4 2 2
+ 6*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 3 1 4 3 4
- ---*f(v,v) *a1 *a13*a18*a4 *b1 + ---*f(v,v) *a13 *a4 *b1
2 2
3 3 2 3 3 3
- 2*f(v,v) *a1 *a13*a18*a4 *b1*u + f(v,v) *a1*a13 *a4 *b1*u
2 4 2 2 2 3 2 2
- 2*f(v,v) *a1 *a13*a18*a4*b1*u - 2*f(v,v) *a1 *a13 *a4 *b1*u
3 3 3 7
- 4*f(v,v)*a1 *a13 *a4*b1*u )/a1
5 5 3 2
df(v,s)=(u *a1 *a13*b1*v + u *f(v,v)*a1 *a18*b1*v + u *f(v,v)*a1 *a13 *a4*b1*v
2x x x
4 2 2 4
+ 6*u *a1 *a13 *b1*u*v - v *f(v,v) *a1 *a18*a4*b1
x x
2 2 2 2 5
+ 2*v *f(v,v) *a1 *a13 *a4 *b1 - 2*v *f(v,v)*a1 *a18*b1*u
x x
3 2 4
+ 4*v *f(v,v)*a1 *a13 *a4*b1*u + f(v ,v )*a1 *a13*a4*b1*v
x x x
4 4
+ f(v,v )*a1 *a13*a4*b1*v + 2*f(v,v )*f(v,v)*a1 *a18*a4*b1*v
2x x
2 2 2 5
- f(v,v )*f(v,v)*a1 *a13 *a4 *b1*v + 2*f(v,v )*a1 *a18*b1*u*v
x x
3 2 1 3 2 2
+ 2*f(v,v )*a1 *a13 *a4*b1*u*v + ---*f(v,v) *a1 *a13*a18*a4 *b1*v
x 2
1 3 3 3 2 3
- ---*f(v,v) *a13 *a4 *b1*v + 2*f(v,v) *a1 *a13*a18*a4*b1*u*v
2
2 3 2 4 2
- f(v,v) *a1*a13 *a4 *b1*u*v + 2*f(v,v)*a1 *a13*a18*b1*u *v
2 3 2 3 3 3 6
+ 2*f(v,v)*a1 *a13 *a4*b1*u *v + 4*a1 *a13 *b1*u *v)/a1