Solution 7 to problem l112o13
Expressions |
Parameters |
Relevance |
Back to problem l112o13
Expressions
The solution is given through the following expressions:
b42=0
b41=0
2 1 2
- 3*a0 *b22 - a0*a4*b39 + ---*a4 *b9
2
b40=---------------------------------------
a0*a4
b38=0
b37=0
b36=0
b35=0
1 1
- ---*a0*b19 - a4*b31 + ---*a4*b9
2 2
b34=------------------------------------
a4
1 1
- ---*a0*b19 + ---*a4*b9
2 2
b33=---------------------------
a4
- a0*b19 + a4*b9
b32=-------------------
a4
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
1
a0*b10 - ---*a0*b9
3
b24=--------------------
a4
1
---*a3*b22
2
b23=------------
a0
1
3*a0*a3*b22 + ---*a3*a4*b19
2
b21=-----------------------------
a0*a4
b20=0
1
---*a4*b9
2
b18=-----------
a0
a3*b19
b17=--------
a4
1 1
---*a0*a3*b19 - a3*a4*b10 + ---*a3*a4*b9
2 2
b16=------------------------------------------
a0*a4
1 1
---*a0*a3*b19 + ---*a3*a4*b10
2 2
b15=-------------------------------
a0*a4
b14=0
b13=0
b12=0
b11= - 2*b10 + b9
1
b8=---*b9
2
1
- a3*b10 + ---*a3*b9
2
b7=-----------------------
a4
1
---*a3*b9
2
b6=-----------
a4
b5=0
b4=0
b3=0
b2=0
1
---*a0*b9
6
b1=-----------
a4
a8=0
a7=0
1
---*a3*a4
2
a5=-----------
a0
a2=0
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, b31, b22, b19, b10, b9, a3, a0, a4
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
df(u,t)=
2 1 2
u *a0 + u *a0*a6 + f(v,v )*a0*a3 + ---*f(v,v) *a3*a4 + f(v,v)*a0*a4*u
x x x 2
------------------------------------------------------------------------
a0
df(v,t)=v *a6
x
1 2 1
df(u,s)=(---*u *a0 *b9 + ---*u *f(v,v)*a0*a4*b9 + u *f(v,v )*a0*a4*b9
6 3x 2 2x x x
1 2 2 1
+ ---*u *f(v,v) *a4 *b9 + ---*f(v ,v )*a0*a3*b9
2 x 2 x 2x
1 1
+ ---*f(v ,v )*f(v,v)*a0*a3*b19 + ---*f(v ,v )*f(v,v)*a3*a4*b10
2 x x 2 x x
1
+ f(v ,v )*a0*a4*b10*u - f(v,v )*a0*a3*b10 + ---*f(v,v )*a0*a3*b9
x x 3x 2 3x
1
+ ---*f(v,v )*f(v,v)*a0*a3*b19 - f(v,v )*f(v,v)*a3*a4*b10
2 2x 2x
1
+ ---*f(v,v )*f(v,v)*a3*a4*b9 - 2*f(v,v )*a0*a4*b10*u
2 2x 2x
2
+ f(v,v )*a0*a4*b9*u + f(v,v ) *a0*a3*b19
2x x
2 1 2
+ 3*f(v,v )*f(v,v) *a0*a3*b22 + ---*f(v,v )*f(v,v) *a3*a4*b19
x 2 x
1 4
+ f(v,v )*f(v,v)*a0*a4*b19*u + ---*f(v,v) *a3*a4*b22
x 2
3
+ f(v,v) *a0*a4*b22*u)/(a0*a4)
2 1 2
df(v,s)=(v *a0 *b10 - ---*v *a0 *b9 + v *f(v,v)*a0*a4*b31
3x 3 3x 2x
2 2
- v *f(v,v )*a0 *b19 + v *f(v,v )*a0*a4*b9 + v *f(v,v) *a0*a4*b39
x x x x x
1 2 1
- ---*f(v ,v )*a0 *b19*v + ---*f(v ,v )*a0*a4*b9*v
2 x x 2 x x
1 2
- ---*f(v,v )*a0 *b19*v - f(v,v )*a0*a4*b31*v
2 2x 2x
1 2
+ ---*f(v,v )*a0*a4*b9*v - 3*f(v,v )*f(v,v)*a0 *b22*v
2 2x x
1 2
- f(v,v )*f(v,v)*a0*a4*b39*v + ---*f(v,v )*f(v,v)*a4 *b9*v)/(a0*a4)
x 2 x