Solution 6 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
b42=0
b41=0
3 2 2
- ---*a2 *a4 *b24
8
b40=--------------------
4
a12
b39=0
b38=0
3 2
---*a2 *a4*b24
4
b37=----------------
3
a12
b36=0
3 2
---*a2 *a4*b24
8
b35=----------------
3
a12
b34=0
b33=0
3
---*a2*a4*b24
2
b32=---------------
2
a12
b31=0
b30=0
b29=0
3 2
- ---*a2 *b24
4
b28=----------------
2
a12
b27=0
3
- ---*a2*b24
2
b26=---------------
a12
b25=0
b23=0
b22=0
9 2 3
- ----*a2 *a4 *b24
16
b21=---------------------
5
a12
b20=0
3 2 2
---*a2 *a4 *b24
2
b19=-----------------
4
a12
9 2 2
----*a2 *a4 *b24
16
b18=------------------
4
a12
b17=0
3 2
- ---*a2*a4 *b24
4
b16=-------------------
3
a12
3 2
- ---*a2*a4 *b24
4
b15=-------------------
3
a12
b14=0
3 2
- ---*a2 *a4*b24
4
b13=-------------------
3
a12
3 2
- ---*a2 *a4*b24
2
b12=-------------------
3
a12
3
---*a2*a4*b24
2
b11=---------------
2
a12
3
---*a2*a4*b24
2
b10=---------------
2
a12
3
---*a2*a4*b24
2
b9=---------------
2
a12
3
---*a2*a4*b24
4
b8=---------------
2
a12
b7=0
- 3*a4*b24
b6=-------------
a12
b5=0
3 2
---*a2 *b24
4
b4=-------------
2
a12
3
- ---*a2*b24
2
b3=---------------
a12
3
- ---*a2*b24
2
b2=---------------
a12
b1=b24
a19=0
a18=0
a2*a4
a17=-------
a12
a16=0
a15=0
a14=0
a13= - a2
a11=0
a10=0
3 2
---*a2*a4
2
a9=------------
2
a12
a8=0
- a2*a4
a7=----------
a12
3
- ---*a2*a4
2
a6=--------------
a12
a5=2*a4
a3=0
a1= - a12
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:
b24,a4,a2,a12
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 3 2 2
df(u,t)=( - u *a12 - ---*u *f(v,v)*a12*a2*a4 + u *a12 *a2*u + f(v ,v )*a12 *a4
2x 2 x x x x
2 3 2
+ 2*f(v,v )*a12 *a4 + ---*f(v,v )*f(v,v)*a2*a4 - f(v,v )*a12*a2*a4*u
2x 2 x x
2
)/a12
2
- u *a12*a2*v + v *a12 + f(v,v )*a2*a4*v
x 2x x
df(v,t)=---------------------------------------------
a12
5 3 3 3 4
df(u,s)=(u *a12 *b24 + ---*u *f(v,v)*a12 *a2*a4*b24 - ---*u *a12 *a2*b24*u
3x 4 2x 2 2x
3 2 4 3 3
- ---*u *a12 *a2*b24 + ---*u *f(v,v )*a12 *a2*a4*b24
2 x 2 x x
9 2 2 2 3 2 2
+ ----*u *f(v,v) *a12*a2 *a4 *b24 - ---*u *f(v,v)*a12 *a2 *a4*b24*u
16 x 2 x
3 3 2 2 4
+ ---*u *a12 *a2 *b24*u - 3*f(v ,v )*a12 *a4*b24
4 x x 2x
3 2 2 3 3
- ---*f(v ,v )*f(v,v)*a12 *a2*a4 *b24 + ---*f(v ,v )*a12 *a2*a4*b24*u
4 x x 2 x x
3 2 2 3 3
- ---*f(v,v )*f(v,v)*a12 *a2*a4 *b24 + ---*f(v,v )*a12 *a2*a4*b24*u
4 2x 2 2x
9 2 2 3
- ----*f(v,v )*f(v,v) *a2 *a4 *b24
16 x
3 2 2
+ ---*f(v,v )*f(v,v)*a12*a2 *a4 *b24*u
2 x
3 2 2 2 5
- ---*f(v,v )*a12 *a2 *a4*b24*u )/a12
4 x
3 3 3 2
df(v,s)=( - ---*u *v *a12 *a2*b24 + ---*u *f(v,v)*a12*a2 *a4*b24*v
2 x x 8 x
3 2 2 4
- ---*u *a12 *a2 *b24*u*v + v *a12 *b24
4 x 3x
3 2 3 2 2
+ ---*v *f(v,v )*a12 *a2*a4*b24 - ---*f(v,v )*f(v,v)*a2 *a4 *b24*v
2 x x 8 x
3 2 4
+ ---*f(v,v )*a12*a2 *a4*b24*u*v)/a12
4 x