Solution 14 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
b42=0
b41=0
1 2 2
- ---*a14 *a4 *b1
2
b40=--------------------
4
a1
1 2 2
---*a14 *a4 *b1
4
b39=-----------------
4
a1
b38=0
2
- a14 *a4*b1
b37=---------------
3
a1
2
a14 *a4*b1
b36=------------
3
a1
1 2
- ---*a14 *a4*b1
2
b35=-------------------
3
a1
1
- ---*a14*a4*b1
2
b34=------------------
2
a1
1
- ---*a14*a4*b1
2
b33=------------------
2
a1
a14*a4*b1
b32=-----------
2
a1
b31=0
b30=0
2
a14 *b1
b29=---------
2
a1
2
- a14 *b1
b28=------------
2
a1
b27=0
a14*b1
b26=--------
a1
1
- ---*a14*b1
2
b25=---------------
a1
b24=0
b23=0
b22=0
2 3
a14 *a4 *b1
b21=-------------
5
a1
b20=0
2 2
3*a14 *a4 *b1
b19=---------------
4
a1
5 2 2
---*a14 *a4 *b1
4
b18=-----------------
4
a1
2
2*a14*a4 *b1
b17=--------------
3
a1
2
2*a14*a4 *b1
b16=--------------
3
a1
2
2*a14*a4 *b1
b15=--------------
3
a1
b14=0
2
2*a14 *a4*b1
b13=--------------
3
a1
2
4*a14 *a4*b1
b12=--------------
3
a1
3*a14*a4*b1
b11=-------------
2
a1
3*a14*a4*b1
b10=-------------
2
a1
5*a14*a4*b1
b9=-------------
2
a1
2*a14*a4*b1
b8=-------------
2
a1
a4*b1
b7=-------
a1
3*a4*b1
b6=---------
a1
b5=0
2
3*a14 *b1
b4=-----------
2
a1
3*a14*b1
b3=----------
a1
3*a14*b1
b2=----------
a1
1
---*a18*a4
2
a19=------------
a1
2*a1*a18 - a14*a16
a17=--------------------
a14
a15=0
1
a13= - ---*a14
2
a12=0
1 2
- ---*a18*a4
2
a11=----------------
2
a1
- a18*a4
a10=-----------
a1
2 2 2
- 2*a1 *a18*a4 + a14 *a4
a9=----------------------------
2
a1 *a14
a8=0
a14*a4
a7=--------
a1
3
---*a14*a4
2
a6=------------
a1
a5=a4
a3=0
a2=2*a14
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,a16,a4,a14,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 3 2 2 2
df(u,t)=(u *a1 *a14 + ---*u *f(v,v)*a1*a14 *a4 + 2*u *a1 *a14 *u
2x 2 x x
2 2
+ f(v ,v )*a1 *a14*a4 + f(v,v )*a1 *a14*a4
x x 2x
2 2 2
- 2*f(v,v )*f(v,v)*a1 *a18*a4 + f(v,v )*f(v,v)*a14 *a4
x x
2 1 3 2
+ f(v,v )*a1*a14 *a4*u - ---*f(v,v) *a14*a18*a4
x 2
2 2
- f(v,v) *a1*a14*a18*a4*u)/(a1 *a14)
1 2 2
df(v,t)=( - ---*u *a1*a14 *v + v *f(v,v)*a1*a14*a16 + v *a1*a14 *u
2 x x x
2
+ 2*f(v,v )*a1 *a18*v - f(v,v )*a1*a14*a16*v
x x
1 2
+ ---*f(v,v) *a14*a18*a4*v + f(v,v)*a1*a14*a18*u*v)/(a1*a14)
2
5 3 4
df(u,s)=(u *a1 *b1 + 2*u *f(v,v)*a1 *a14*a4*b1 + 3*u *a1 *a14*b1*u
3x 2x 2x
2 4 3
+ 3*u *a1 *a14*b1 + 5*u *f(v,v )*a1 *a14*a4*b1
x x x
5 2 2 2 2 2
+ ---*u *f(v,v) *a1*a14 *a4 *b1 + 4*u *f(v,v)*a1 *a14 *a4*b1*u
4 x x
3 2 2 4
+ 3*u *a1 *a14 *b1*u + 3*f(v ,v )*a1 *a4*b1
x x 2x
2 2 3
+ 2*f(v ,v )*f(v,v)*a1 *a14*a4 *b1 + 3*f(v ,v )*a1 *a14*a4*b1*u
x x x x
4 2 2
+ f(v,v )*a1 *a4*b1 + 2*f(v,v )*f(v,v)*a1 *a14*a4 *b1
3x 2x
3 2 2 2
+ 3*f(v,v )*a1 *a14*a4*b1*u + 2*f(v,v ) *a1 *a14*a4 *b1
2x x
2 2 3 2 2
+ f(v,v )*f(v,v) *a14 *a4 *b1 + 3*f(v,v )*f(v,v)*a1*a14 *a4 *b1*u
x x
2 2 2 5
+ 2*f(v,v )*a1 *a14 *a4*b1*u )/a1
x
1 3 3
df(v,s)=( - ---*u *a1 *a14*b1*v + u *v *a1 *a14*b1
2 2x x x
1 2 2 2
- ---*u *f(v,v)*a1*a14 *a4*b1*v - u *a1 *a14 *b1*u*v
2 x x
2 1 2 2 2
+ v *f(v,v )*a1 *a14*a4*b1 + ---*v *f(v,v) *a14 *a4 *b1
x x 4 x
2 2 2 2
+ v *f(v,v)*a1*a14 *a4*b1*u + v *a1 *a14 *b1*u
x x
1 2 1 2
- ---*f(v ,v )*a1 *a14*a4*b1*v - ---*f(v,v )*a1 *a14*a4*b1*v
2 x x 2 2x
1 2 2 2 4
- ---*f(v,v )*f(v,v)*a14 *a4 *b1*v - f(v,v )*a1*a14 *a4*b1*u*v)/a1
2 x x