Solution 24 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
1
---*a4*b41
2
b42=------------
a1
4*a1*b41 - a14*b39
b40=--------------------
a14
b38=0
1 2
- ---*a14 *a4*b1
2
b37=-------------------
3
a1
2
a14 *a4*b1
b36=------------
3
a1
1 2
- ---*a14 *a4*b1
4
b35=-------------------
3
a1
1
- ---*a14*a4*b1
4
b34=------------------
2
a1
1
- ---*a14*a4*b1
4
b33=------------------
2
a1
a14*a4*b1
b32=-----------
2
a1
b31=0
b30=0
2
a14 *b1
b29=---------
2
a1
1 2
- ---*a14 *b1
2
b28=----------------
2
a1
b27=0
a14*b1
b26=--------
a1
1
- ---*a14*b1
4
b25=---------------
a1
b24=0
1 2
- ---*a4 *b41
2
b23=----------------
2
a1
- a4*b41
b22=-----------
a1
5 3 3 3
- 4*a1 *a4*b41 + ---*a14 *a4 *b1
4
b21=-----------------------------------
5
a1 *a14
b20=0
5 2 2
---*a14 *a4 *b1
2
b19=-----------------
4
a1
2 2
a14 *a4 *b1
b18=-------------
4
a1
2
2*a14*a4 *b1
b17=--------------
3
a1
7 2
---*a14*a4 *b1
4
b16=----------------
3
a1
7 2
---*a14*a4 *b1
4
b15=----------------
3
a1
b14=0
2
2*a14 *a4*b1
b13=--------------
3
a1
7 2
---*a14 *a4*b1
2
b12=----------------
3
a1
3*a14*a4*b1
b11=-------------
2
a1
3*a14*a4*b1
b10=-------------
2
a1
5*a14*a4*b1
b9=-------------
2
a1
7
---*a14*a4*b1
4
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
a19=0
a18=0
1
- ---*a14*a4
4
a17=---------------
a1
1
---*a14*a4
2
a16=------------
a1
a15=0
1
a13= - ---*a14
4
a12=0
a11=0
a10=0
3 2
---*a14*a4
4
a9=-------------
2
a1
a8=0
a14*a4
a7=--------
a1
5
---*a14*a4
4
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:
b39,b41,b1,a4,a14,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 5 2 2
df(u,t)=(u *a1 + ---*u *f(v,v)*a1*a14*a4 + 2*u *a1 *a14*u + f(v ,v )*a1 *a4
2x 4 x x x x
2 3 2
+ f(v,v )*a1 *a4 + ---*f(v,v )*f(v,v)*a14*a4 + f(v,v )*a1*a14*a4*u)/
2x 4 x x
2
a1
df(v,t)=
1 1 1
- ---*u *a1*a14*v + ---*v *f(v,v)*a14*a4 + v *a1*a14*u - ---*f(v,v )*a14*a4*v
4 x 2 x x 4 x
--------------------------------------------------------------------------------
a1
5 7 3 2 4 2
df(u,s)=(u *a1 *a14*b1 + ---*u *f(v,v)*a1 *a14 *a4*b1 + 3*u *a1 *a14 *b1*u
3x 4 2x 2x
2 4 2 3 2
+ 3*u *a1 *a14 *b1 + 5*u *f(v,v )*a1 *a14 *a4*b1
x x x
2 3 2 7 2 3
+ u *f(v,v) *a1*a14 *a4 *b1 + ---*u *f(v,v)*a1 *a14 *a4*b1*u
x 2 x
3 3 2 4
+ 3*u *a1 *a14 *b1*u + 3*f(v ,v )*a1 *a14*a4*b1
x x 2x
7 2 2 2 3 2
+ ---*f(v ,v )*f(v,v)*a1 *a14 *a4 *b1 + 3*f(v ,v )*a1 *a14 *a4*b1*u
4 x x x x
4 7 2 2 2
+ f(v,v )*a1 *a14*a4*b1 + ---*f(v,v )*f(v,v)*a1 *a14 *a4 *b1
3x 4 2x
3 2 2 2 2 2
+ 3*f(v,v )*a1 *a14 *a4*b1*u + 2*f(v,v ) *a1 *a14 *a4 *b1
2x x
2 5 3 2 3 3
- 4*f(v,v )*f(v,v) *a1 *a4*b41 + ---*f(v,v )*f(v,v) *a14 *a4 *b1
x 4 x
5 3 2 2 3 2
+ ---*f(v,v )*f(v,v)*a1*a14 *a4 *b1*u + 2*f(v,v )*a1 *a14 *a4*b1*u
2 x x
1 4 3 2 3 4 5
- ---*f(v,v) *a1 *a14*a4 *b41 - f(v,v) *a1 *a14*a4*b41*u)/(a1 *a14)
2
1 2 2 2 2
df(v,s)=( - ---*u *a1 *a14 *b1*v + u *v *a1 *a14 *b1
4 2x x x
1 3 1 3
- ---*u *f(v,v)*a14 *a4*b1*v - ---*u *a1*a14 *b1*u*v
4 x 2 x
2 2 3
+ v *f(v,v )*a1*a14 *a4*b1 + v *f(v,v) *a1 *a14*b39
x x x
3 3 2
+ v *f(v,v)*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
4 x x 4 2x
4 3
+ 4*f(v,v )*f(v,v)*a1 *b41*v - f(v,v )*f(v,v)*a1 *a14*b39*v
x x
1 3 1 3 2
- ---*f(v,v )*a14 *a4*b1*u*v + ---*f(v,v) *a1 *a14*a4*b41*v
2 x 2
2 3 3
+ f(v,v) *a1 *a14*b41*u*v)/(a1 *a14)