Solution 1 to problem l12o13
Expressions |
Parameters |
Relevance |
Back to problem l12o13
Expressions
The solution is given through the following expressions:
b36=0
2 2
a3 *a5*b1 - a3 *a5*b17
b35=------------------------
3
a0
b34=0
2
3*a3 *b17
b33=-----------
2
a0
2 2
- 2*a3*a5 *b1 + 2*a3*a5 *b17
b32=-------------------------------
3
a0
4*a3*a5*b1 - 4*a3*a5*b17
b31=--------------------------
2
a0
- 6*a3*a5*b17
b30=----------------
2
a0
2*a3*a5*b1 - 2*a3*a5*b17
b29=--------------------------
2
a0
b28=0
3*a3*b17
b27=----------
a0
6*a3*b17
b26=----------
a0
3*a3*b17
b25=----------
a0
3 3
a5 *b1 - a5 *b17
b24=------------------
3
a0
2
3*a5 *b17
b23=-----------
2
a0
2 2
- 6*a5 *b1 + 6*a5 *b17
b22=-------------------------
2
a0
- 3*a5*b17
b21=-------------
a0
- 6*a5*b17
b20=-------------
a0
- a5*b1 - 2*a5*b17
b19=---------------------
a0
2*a5*b1 - 2*a5*b17
b18=--------------------
a0
3 3
a3 *b1 - a3 *b17
b16=------------------
3
a0
2 2
- 2*a3 *a5*b1 + 2*a3 *a5*b17
b15=-------------------------------
3
a0
2 2
6*a3 *b1 - 6*a3 *b17
b14=----------------------
2
a0
2
3*a3 *b1
b13=----------
2
a0
2 2
a3*a5 *b1 - a3*a5 *b17
b12=------------------------
3
a0
- 2*a3*a5*b1 + 2*a3*a5*b17
b11=-----------------------------
2
a0
- 10*a3*a5*b1 + 4*a3*a5*b17
b10=------------------------------
2
a0
2*a3*b1 - 2*a3*b17
b9=--------------------
a0
2*a3*b1 + a3*b17
b8=------------------
a0
6*a3*b1
b7=---------
a0
3*a3*b1
b6=---------
a0
b5=0
2
3*a5 *b1
b4=----------
2
a0
- 9*a5*b1
b3=------------
a0
- 3*a5*b1
b2=------------
a0
a6=0
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:
b17, b1, a3, a4, a5, a0
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
df(u,t)=u *a0 + u *a4 + f(v,v)*a3*u
x x
2
df(v,t)=v *a4 + a5*u *v
x
3 2 2 2
df(u,s)=(u *a0 *b1 + 3*u *f(v,v)*a0 *a3*b1 - 3*u *a0 *a5*b1*u
3x 2x 2x
2 2 2 2 2
- 9*u *a0 *a5*b1*u + 6*u *f(v,v )*a0 *a3*b1 + 3*u *f(v,v) *a0*a3 *b1
x x x x
2 2
- 10*u *f(v,v)*a0*a3*a5*b1*u + 4*u *f(v,v)*a0*a3*a5*b17*u
x x
2 4 2 2
+ 3*u *a0*a5 *b1*u + 2*f(v ,v )*a0 *a3*b1*u + f(v ,v )*a0 *a3*b17*u
x x x x x
2 2
+ 2*f(v,v )*a0 *a3*b1*u - 2*f(v,v )*a0 *a3*b17*u
2x 2x
2 2
+ 6*f(v,v )*f(v,v)*a0*a3 *b1*u - 6*f(v,v )*f(v,v)*a0*a3 *b17*u
x x
3 3
- 2*f(v,v )*a0*a3*a5*b1*u + 2*f(v,v )*a0*a3*a5*b17*u
x x
3 3 3 3 2 2 3
+ f(v,v) *a3 *b1*u - f(v,v) *a3 *b17*u - 2*f(v,v) *a3 *a5*b1*u
2 2 3 2 5
+ 2*f(v,v) *a3 *a5*b17*u + f(v,v)*a3*a5 *b1*u
2 5 3
- f(v,v)*a3*a5 *b17*u )/a0
2 2 2 2
df(v,s)=(2*u *a0 *a5*b1*u*v - 2*u *a0 *a5*b17*u*v - u *a0 *a5*b1*v
2x 2x x
2 2 2
- 2*u *a0 *a5*b17*v - 6*u *v *a0 *a5*b17*u
x x x
+ 2*u *f(v,v)*a0*a3*a5*b1*u*v - 2*u *f(v,v)*a0*a3*a5*b17*u*v
x x
2 3 2 3 3
- 6*u *a0*a5 *b1*u *v + 6*u *a0*a5 *b17*u *v + v *a0 *b17
x x 3x
2 2 2
+ 3*v *f(v,v)*a0 *a3*b17 - 3*v *a0 *a5*b17*u
2x 2x
2 2 2
+ 6*v *f(v,v )*a0 *a3*b17 + 3*v *f(v,v) *a0*a3 *b17
x x x
2 2 4
- 6*v *f(v,v)*a0*a3*a5*b17*u + 3*v *a0*a5 *b17*u
x x
2 2
+ 3*f(v ,v )*a0 *a3*b17*v + 4*f(v,v )*a0*a3*a5*b1*u *v
x x x
2 2 2 2
- 4*f(v,v )*a0*a3*a5*b17*u *v + f(v,v) *a3 *a5*b1*u *v
x
2 2 2 2 4
- f(v,v) *a3 *a5*b17*u *v - 2*f(v,v)*a3*a5 *b1*u *v
2 4 3 6 3 6 3
+ 2*f(v,v)*a3*a5 *b17*u *v + a5 *b1*u *v - a5 *b17*u *v)/a0