Solution 2 to problem l112o12
Expressions |
Parameters |
Relevance |
Back to problem l112o12
Expressions
The solution is given through the following expressions:
a5*a8*b7
b19=-----------------
a3*a4 - 2*a3*a8
a8*b7
b18=-------
a3
a8*b7
b17=-----------
a4 - 2*a8
b16=0
2
- 2*a4*a8 *b7
b15=-----------------------
a3*a4*a5 - 2*a3*a5*a8
b14=0
a4*a8*b7
b13=-------------------
2*a4*a5 - 4*a5*a8
b12=0
2
a5 *b7
b11=-----------------
a3*a4 - 2*a3*a8
a5*b7
b10=-------
a3
3*a5*b7
b9=-----------
a4 - 2*a8
- 2*a4*a8*b7
b8=-----------------
a3*a4 - 2*a3*a8
a4*b7 - a8*b7
b6=---------------
a4 - 2*a8
a3*b7
b5=-------------
2*a4 - 4*a8
a3*b7
b4=-------------
2*a4 - 4*a8
b3=0
- 2*a4*a8*b7
b2=-----------------
a4*a5 - 2*a5*a8
a2=0
a3*a4
a0=-------
2*a5
a4*a8
a7=-------
a5
a3*a4*b7
b1=-------------------
4*a4*a5 - 8*a5*a8
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:
b7, a5, a8, a4, a3
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
df(u,t)=
1 2 2
---*u *a3*a4 + u *a5*a6 + f(v,v )*a3*a5 + f(v,v) *a5 + f(v,v)*a4*a5*u
2 x x x
------------------------------------------------------------------------
a5
v *a5*a6 + f(v,v)*a5*a8*v + a4*a8*u*v
x
df(v,t)=---------------------------------------
a5
1 2
df(u,s)=(---*u *a3 *a4*b7 + u *f(v,v)*a3*a4*a5*b7 - u *f(v,v)*a3*a5*a8*b7
4 2x x x
1 2
- 2*u *a3*a4*a8*b7*u + ---*f(v ,v )*a3 *a5*b7
x 2 x x
1 2 2
+ ---*f(v,v )*a3 *a5*b7 + 3*f(v,v )*f(v,v)*a3*a5 *b7
2 2x x
3 3
+ f(v,v )*a3*a4*a5*b7*u - 2*f(v,v )*a3*a5*a8*b7*u + f(v,v) *a5 *b7
x x
2 2 2 2
+ f(v,v) *a4*a5 *b7*u - 2*f(v,v) *a5 *a8*b7*u
2
- 2*f(v,v)*a4*a5*a8*b7*u )/(a3*a4*a5 - 2*a3*a5*a8)
1 2 2
df(v,s)=(---*u *a3*a4*a8*b7*v + f(v,v )*a3*a5*a8*b7*v + f(v,v) *a5 *a8*b7*v
2 x x
2 2 2
+ f(v,v)*a4*a5*a8*b7*u*v - 2*f(v,v)*a5*a8 *b7*u*v - 2*a4*a8 *b7*u *v)
/(a3*a4*a5 - 2*a3*a5*a8)