Solution 21 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
2*a13*a19*a4*b1
b42=-----------------
3
a1
4*a13*a19*b1
b41=--------------
2
a1
2 2
4*a13 *a4 *b1
b40=---------------
4
a1
2 2
4*a13 *a4 *b1
b39=---------------
4
a1
b38=0
2
8*a13 *a4*b1
b37=--------------
3
a1
2
16*a13 *a4*b1
b36=---------------
3
a1
2
4*a13 *a4*b1
b35=--------------
3
a1
a13*a4*b1
b34=-----------
2
a1
a13*a4*b1
b33=-----------
2
a1
4*a13*a4*b1
b32=-------------
2
a1
b31=0
b30=0
2
16*a13 *b1
b29=------------
2
a1
2
8*a13 *b1
b28=-----------
2
a1
b27=0
4*a13*b1
b26=----------
a1
a13*b1
b25=--------
a1
b24=0
2
- 2*a13*a19*a4 *b1
b23=---------------------
4
a1
- 4*a13*a19*a4*b1
b22=--------------------
3
a1
2 3
4*a13 *a4 *b1
b21=---------------
5
a1
b20=0
2 2
24*a13 *a4 *b1
b19=----------------
4
a1
2 2
8*a13 *a4 *b1
b18=---------------
4
a1
2
8*a13*a4 *b1
b17=--------------
3
a1
2
5*a13*a4 *b1
b16=--------------
3
a1
2
5*a13*a4 *b1
b15=--------------
3
a1
b14=0
2
32*a13 *a4*b1
b13=---------------
3
a1
2
40*a13 *a4*b1
b12=---------------
3
a1
12*a13*a4*b1
b11=--------------
2
a1
12*a13*a4*b1
b10=--------------
2
a1
20*a13*a4*b1
b9=--------------
2
a1
5*a13*a4*b1
b8=-------------
2
a1
a4*b1
b7=-------
a1
3*a4*b1
b6=---------
a1
b5=0
2
48*a13 *b1
b4=------------
2
a1
12*a13*b1
b3=-----------
a1
12*a13*b1
b2=-----------
a1
a18=0
a13*a4
a17=--------
a1
2*a13*a4
a16=----------
a1
a15=0
a14=4*a13
a12=0
- a19*a4
a11=-----------
a1
a10=0
2
a13*a4
a9=---------
2
a1
a8=0
4*a13*a4
a7=----------
a1
3*a13*a4
a6=----------
a1
a5=a4
a3=0
a2=8*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,a19,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 2
df(u,t)=(u *a1 + 3*u *f(v,v)*a1*a13*a4 + 8*u *a1 *a13*u + f(v ,v )*a1 *a4
2x x x x x
2 2
+ f(v,v )*a1 *a4 + f(v,v )*f(v,v)*a13*a4 + 4*f(v,v )*a1*a13*a4*u
2x x x
3 2
- f(v,v) *a1*a19*a4)/a1
df(v,t)=(u *a1*a13*v + 2*v *f(v,v)*a13*a4 + 4*v *a1*a13*u + f(v,v )*a13*a4*v
x x x x
2
+ f(v,v) *a1*a19*v)/a1
5 3 4
df(u,s)=(u *a1 *b1 + 5*u *f(v,v)*a1 *a13*a4*b1 + 12*u *a1 *a13*b1*u
3x 2x 2x
2 4 3
+ 12*u *a1 *a13*b1 + 20*u *f(v,v )*a1 *a13*a4*b1
x x x
2 2 2 2 2
+ 8*u *f(v,v) *a1*a13 *a4 *b1 + 40*u *f(v,v)*a1 *a13 *a4*b1*u
x x
3 2 2 4
+ 48*u *a1 *a13 *b1*u + 3*f(v ,v )*a1 *a4*b1
x x 2x
2 2 3
+ 5*f(v ,v )*f(v,v)*a1 *a13*a4 *b1 + 12*f(v ,v )*a1 *a13*a4*b1*u
x x x x
4 2 2
+ f(v,v )*a1 *a4*b1 + 5*f(v,v )*f(v,v)*a1 *a13*a4 *b1
3x 2x
3 2 2 2
+ 12*f(v,v )*a1 *a13*a4*b1*u + 8*f(v,v ) *a1 *a13*a4 *b1
2x x
2 2 3 2 2
+ 4*f(v,v )*f(v,v) *a13 *a4 *b1 + 24*f(v,v )*f(v,v)*a1*a13 *a4 *b1*u
x x
2 2 2 4 2
+ 32*f(v,v )*a1 *a13 *a4*b1*u - 2*f(v,v) *a1*a13*a19*a4 *b1
x
3 2 5
- 4*f(v,v) *a1 *a13*a19*a4*b1*u)/a1
3 3 2
df(v,s)=(u *a1 *a13*b1*v + 4*u *v *a1 *a13*b1 + 4*u *f(v,v)*a1*a13 *a4*b1*v
2x x x x
2 2 2
+ 8*u *a1 *a13 *b1*u*v + 4*v *f(v,v )*a1 *a13*a4*b1
x x x
2 2 2 2
+ 4*v *f(v,v) *a13 *a4 *b1 + 16*v *f(v,v)*a1*a13 *a4*b1*u
x x
2 2 2 2
+ 16*v *a1 *a13 *b1*u + f(v ,v )*a1 *a13*a4*b1*v
x x x
2 2 2
+ f(v,v )*a1 *a13*a4*b1*v + 4*f(v,v )*f(v,v)*a13 *a4 *b1*v
2x x
2 3
+ 8*f(v,v )*a1*a13 *a4*b1*u*v + 2*f(v,v) *a1*a13*a19*a4*b1*v
x
2 2 4
+ 4*f(v,v) *a1 *a13*a19*b1*u*v)/a1