Solution 1 to problem l1o23
Expressions |
Parameters |
Relevance |
Back to problem l1o23
Expressions
The solution is given through the following expressions:
3 2
- ---*a4*a8 *b12
8
b21=-------------------
3
a6
3
- ---*a4*a8*b12
4
b20=------------------
2
a6
b19=0
3 3 3 3
- ---*a1*a8 *b12 + ---*a6*a8 *b12
4 8
b18=------------------------------------
4
a6
3 2
---*a8 *b12
4
b17=-------------
2
a6
9 2 3 2
- ---*a1*a8 *b12 + ---*a6*a8 *b12
4 2
b16=------------------------------------
3
a6
3
---*a8*b12
2
b15=------------
a6
3
---*a8*b12
2
b14=------------
a6
3 3
- ---*a1*a8*b12 + ---*a6*a8*b12
4 4
b13=----------------------------------
2
a6
b11=0
b10=0
3
---*a4*a8*b12
2
b9=---------------
2
a6
3
---*a4*a8*b12
4
b8=---------------
2
a6
3
---*a4*b12
2
b7=------------
a6
3
---*a4*b12
2
b6=------------
a6
b5=0
9 2 3 2
---*a1*a8 *b12 - ---*a6*a8 *b12
2 2
b4=---------------------------------
3
a6
9 3
---*a1*a8*b12 - ---*a6*a8*b12
2 2
b3=-------------------------------
2
a6
9 3
---*a1*a8*b12 - ---*a6*a8*b12
2 2
b2=-------------------------------
2
a6
3 1
---*a1*b12 - ---*a6*b12
2 2
b1=-------------------------
a6
1
- ---*a4*a8
4
a10=--------------
a6
1 2 1 2
- ---*a1*a8 + ---*a6*a8
2 4
a9=----------------------------
2
a6
1 1
- ---*a1*a8 + ---*a6*a8
2 2
a7=--------------------------
a6
a5=0
a3=0
2*a1*a8
a2=---------
a6
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:
b12,a4,a8,a6,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
u *a1*a6 + 2*u *a1*a8*u + f(v,v )*a4*a6
2x x x
df(u,t)=------------------------------------------
a6
1 1 2 3 2
df(v,t)=( - ---*u *a1*a6*a8*v + ---*u *a6 *a8*v + v *a6 + v *a6 *a8*u
2 x 2 x 2x x
1 1 2 2 1 2 2 2
- ---*f(v,v)*a4*a6*a8*v - ---*a1*a8 *u *v + ---*a6*a8 *u *v)/a6
4 2 4
3 2 1 3 9
df(u,s)=(---*u *a1*a6 *b12 - ---*u *a6 *b12 + ---*u *a1*a6*a8*b12*u
2 3x 2 3x 2 2x
3 2 9 2 3 2 2
- ---*u *a6 *a8*b12*u + ---*u *a1*a6*a8*b12 - ---*u *a6 *a8*b12
2 2x 2 x 2 x
3 9 2 2
+ ---*u *f(v,v)*a4*a6*a8*b12 + ---*u *a1*a8 *b12*u
4 x 2 x
3 2 2 3 2
- ---*u *a6*a8 *b12*u + ---*f(v ,v )*a4*a6 *b12
2 x 2 x x
3 2 3 3
+ ---*f(v,v )*a4*a6 *b12 + ---*f(v,v )*a4*a6*a8*b12*u)/a6
2 2x 2 x
3 2 3 3
df(v,s)=( - ---*u *a1*a6 *a8*b12*v + ---*u *a6 *a8*b12*v
4 2x 4 2x
3 3 9 2
+ ---*u *v *a6 *a8*b12 - ---*u *a1*a6*a8 *b12*u*v
2 x x 4 x
3 2 2 4 3 3
+ ---*u *a6 *a8 *b12*u*v + v *a6 *b12 + ---*v *a6 *a8*b12*u
2 x 3x 2 2x
3 2 2 2 3 2
+ ---*v *a6 *a8 *b12*u - ---*f(v,v )*a4*a6 *a8*b12*v
4 x 4 x
3 2 3 3 3
- ---*f(v,v)*a4*a6*a8 *b12*u*v - ---*a1*a8 *b12*u *v
8 4
3 3 3 4
+ ---*a6*a8 *b12*u *v)/a6
8