Solution 4 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
1
- ----*a3*a5*b4
12
b42=------------------
2
a0
1 2 1 2
- ---*a0 *a5*b4 + ---*a3 *a7*b4
6 6
b41=----------------------------------
3
a0
1 2 1 2
- ---*a0 *a5*b4 - ----*a3 *a7*b4
6 12
b40=-----------------------------------
2
a0 *a7
b39=0
1
---*a3*a7*b4
2
b38=--------------
2
a0
b37=0
b36=0
b35=0
1
- ----*a3*b4
24
b34=---------------
a7
1
- ----*a3*b4
24
b33=---------------
a7
b32=0
b31=0
1
---*a7*b4
3
b30=-----------
a0
b29=0
b28=0
b27=0
b26=0
1
- ----*a0*b4
24
b25=---------------
a7
b24=0
1 2
- ---*a5 *b4
6
b23=---------------
a0*a7
1
---*a3*a5*b4
2
b22=--------------
2
a0
1
- ---*a3*a5*b4
2
b21=-----------------
a0*a7
1 2 1 2
---*a0 *a5*b4 - ---*a3 *a7*b4
3 3
b20=-------------------------------
3
a0
2 2 2 2
- ---*a0 *a5*b4 + ---*a3 *a7*b4
3 3
b19=----------------------------------
2
a0 *a7
1 2 1 2
- ---*a0 *a5*b4 + ----*a3 *a7*b4
3 12
b18=-----------------------------------
2
a0 *a7
1 2 1 2
- ---*a0 *a5*b4 - ---*a3 *a7*b4
3 6
b17=----------------------------------
2
a0*a7
1 2 1 2
- ---*a0 *a5*b4 - ----*a3 *a7*b4
6 24
b16=-----------------------------------
2
a0*a7
1 2 1 2
- ---*a0 *a5*b4 - ----*a3 *a7*b4
6 24
b15=-----------------------------------
2
a0*a7
1
- ---*a3*a7*b4
3
b14=-----------------
2
a0
a3*b4
b13=-------
a0
a3*b4
b12=-------
a0
b11=0
b10=0
b9=0
1
----*a3*b4
24
b8=------------
a7
1
- ----*a0*a3*b4
24
b7=------------------
2
a7
1
- ---*a0*a3*b4
8
b6=-----------------
2
a7
b5=0
b3=0
b2=0
1
---*a3*a7
2
a8=-----------
a0
- a3*a7
a4=----------
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:
b1, b4, a5, a3, a0, a7, a6
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 2
u *a0 + u *a0*a6 + f(v,v )*a0*a3 + f(v,v) *a0*a5 - f(v,v)*a3*a7*u
x x x
df(u,t)=--------------------------------------------------------------------
a0
1
v *a0*a6 + ---*f(v,v)*a3*a7*v + a0*a7*u*v
x 2
df(v,t)=-------------------------------------------
a0
3 2 1 3
df(u,s)=(u *a0 *a7 *b1 + ----*u *f(v,v)*a0 *a3*a7*b4
3x 24 2x
1 2 3 1 2 2 2
- ---*u *f(v,v) *a0 *a5*a7*b4 + ----*u *f(v,v) *a0*a3 *a7 *b4
3 x 12 x
2 2 3 2 2
+ u *f(v,v)*a0 *a3*a7 *b4*u + u *a0 *a7 *b4*u
x x
1 4 1 4
- ---*f(v ,v )*a0 *a3*b4 - ---*f(v ,v )*f(v,v)*a0 *a5*b4
8 x 2x 6 x x
1 2 2 1 4
- ----*f(v ,v )*f(v,v)*a0 *a3 *a7*b4 - ----*f(v,v )*a0 *a3*b4
24 x x 24 3x
1 4 1 2 2
- ---*f(v,v )*f(v,v)*a0 *a5*b4 - ----*f(v,v )*f(v,v)*a0 *a3 *a7*b4
6 2x 24 2x
1 2 4 1 2 2 2
- ---*f(v,v ) *a0 *a5*b4 - ---*f(v,v ) *a0 *a3 *a7*b4
3 x 6 x
1 2 2
- ---*f(v,v )*f(v,v) *a0 *a3*a5*a7*b4
2 x
2 3
- ---*f(v,v )*f(v,v)*a0 *a5*a7*b4*u
3 x
2 2 2 2 2 2
+ ---*f(v,v )*f(v,v)*a0*a3 *a7 *b4*u + f(v,v )*a0 *a3*a7 *b4*u
3 x x
1 4 2 2 1 3 2
- ---*f(v,v) *a0 *a5 *a7*b4 + ---*f(v,v) *a0*a3*a5*a7 *b4*u
6 2
1 2 2 2 2 1 2 2 3 2
+ ---*f(v,v) *a0 *a5*a7 *b4*u - ---*f(v,v) *a3 *a7 *b4*u
3 3
1 3 3 3 2
- ---*f(v,v)*a0*a3*a7 *b4*u )/(a0 *a7 )
3
1 4 1 3
df(v,s)=( - ----*u *a0 *b4*v - ----*f(v ,v )*a0 *a3*b4*v
24 2x 24 x x
1 3 1 3
- ----*f(v,v )*a0 *a3*b4*v - ---*f(v,v )*f(v,v)*a0 *a5*b4*v
24 2x 6 x
1 2 1 3
- ----*f(v,v )*f(v,v)*a0*a3 *a7*b4*v - ----*f(v,v) *a0*a3*a5*a7*b4*v
12 x 12
1 2 2 1 2 2 2
- ---*f(v,v) *a0 *a5*a7*b4*u*v + ---*f(v,v) *a3 *a7 *b4*u*v
6 6
1 2 2 1 2 2 3 3
+ ---*f(v,v)*a0*a3*a7 *b4*u *v + ---*a0 *a7 *b4*u *v)/(a0 *a7)
2 3