Solution 9 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
10 2
----*a11 *b23
3
b40=---------------
2
a8
5 2
---*a11 *b23
6
b39=--------------
2
a8
10
----*a11*a2*b23
3
b38=-----------------
2
a8
5
---*a11*a2*b23
3
b37=----------------
2
a8
5
---*a11*a2*b23
3
b36=----------------
2
a8
10
----*a11*b23
3
b35=--------------
a8
10*a11*b23
b34=------------
a8
20
----*a11*b23
3
b33=--------------
a8
20
----*a11*b23
3
b32=--------------
a8
20
----*a11*b23
3
b31=--------------
a8
5
---*a11*b23
3
b30=-------------
a8
5 2
---*a2 *b23
6
b29=-------------
2
a8
5 2
---*a2 *b23
3
b28=-------------
2
a8
5
---*a2*b23
3
b27=------------
a8
10
----*a2*b23
3
b26=-------------
a8
10
----*a2*b23
3
b25=-------------
a8
5
---*a2*b23
3
b24=------------
a8
20 3
- ----*a11 *b23
3
b22=------------------
2
a2*a8
20 2
- ----*a11 *b23
3
b21=------------------
2
a8
5 2
- ---*a11 *b23
2
b20=-----------------
2
a8
40 2
- ----*a11 *b23
3
b19=------------------
a2*a8
20 2
- ----*a11 *b23
3
b18=------------------
a2*a8
b17=0
2
- 10*a11 *b23
b16=----------------
a2*a8
b15=0
5
- ---*a11*a2*b23
3
b14=-------------------
2
a8
b13=0
10*a11*b23
b12=------------
a8
b11=0
20
----*a11*b23
3
b10=--------------
a8
b9=0
5
- ---*a11*b23
3
b8=----------------
a8
b7=0
10*a11*b23
b6=------------
a2
20*a11*b23
b5=------------
a2
5 2
---*a2 *b23
6
b4=-------------
2
a8
10
----*a2*b23
3
b3=-------------
a8
5
---*a2*b23
3
b2=------------
a8
b1=b23
a12=2*a11
a10=a2
a9=a2
2
- 4*a11
a7=-----------
a2
a6=0
a5= - a11
a4=0
6*a11*a8
a3=----------
a2
a1=a8
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:
b23,a2,a11,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=(u *a2*a8 - u *f(v,v)*a11*a2 + u *a2 *u + 6*f(v ,v )*a11*a8
3x x x x 2x
2
- 4*f(v,v )*f(v,v)*a11 )/a2
x
df(v,t)=u *a2*v + v *a8 + v *f(v,v)*a11 + v *a2*u + 2*f(v,v )*a11*v
x 3x x x x
2 5 5 2
df(u,s)=(u *a2*a8 *b23 - ---*u *f(v,v)*a11*a2*a8*b23 + ---*u *a2 *a8*b23*u
5x 3 3x 3 3x
10 2 20
+ ----*u *u *a2 *a8*b23 + ----*u *f(v ,v )*a11*a2*a8*b23
3 2x x 3 x x x
5 2 2 5 2
- ---*u *f(v,v) *a11 *a2*b23 - ---*u *f(v,v)*a11*a2 *b23*u
2 x 3 x
5 3 2 2
+ ---*u *a2 *b23*u + 20*f(v ,v )*a11*a8 *b23
6 x 2x 3x
2 2
+ 10*f(v ,v )*a11*a8 *b23 - 10*f(v ,v )*f(v,v)*a11 *a8*b23
x 4x x 2x
20 2
+ 10*f(v ,v )*a11*a2*a8*b23*u - ----*f(v,v )*f(v,v)*a11 *a8*b23
x 2x 3 3x
40 2 20 2 3
- ----*f(v,v )*f(v,v )*a11 *a8*b23 - ----*f(v,v )*f(v,v) *a11 *b23
3 2x x 3 x
20 2 2
- ----*f(v,v )*f(v,v)*a11 *a2*b23*u)/(a2*a8 )
3 x
5 10 10
df(v,s)=(---*u *a2*a8*b23*v + ----*u *v *a2*a8*b23 + ----*u *v *a2*a8*b23
3 3x 3 2x x 3 x 2x
5 5 2 2
+ ---*u *f(v,v)*a11*a2*b23*v + ---*u *a2 *b23*u*v + v *a8 *b23
3 x 3 x 5x
5 5
+ ---*v *f(v,v)*a11*a8*b23 + ---*v *a2*a8*b23*u
3 3x 3 3x
20 20
+ ----*v *f(v,v )*a11*a8*b23 + ----*v *f(v ,v )*a11*a8*b23
3 2x x 3 x x x
20 5 2 2
+ ----*v *f(v,v )*a11*a8*b23 + ---*v *f(v,v) *a11 *b23
3 x 2x 6 x
5 5 2 2
+ ---*v *f(v,v)*a11*a2*b23*u + ---*v *a2 *b23*u
3 x 6 x
10
+ 10*f(v ,v )*a11*a8*b23*v + ----*f(v,v )*a11*a8*b23*v
x 2x 3 3x
10 2 10 2
+ ----*f(v,v )*f(v,v)*a11 *b23*v + ----*f(v,v )*a11*a2*b23*u*v)/a8
3 x 3 x