Solution 1 to problem l21o35
Expressions |
Parameters |
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Back to problem l21o35
Expressions
The solution is given through the following expressions:
5 5 2
----*a2*a7*b23 - ----*a6 *b23
18 72
b40=-------------------------------
2
a8
5 2 2 5 2 5 4
---*a2 *a7 *b23 - ----*a2*a6 *a7*b23 + -----*a6 *b23
6 12 288
b39=------------------------------------------------------
2 2
a6 *a8
5
----*a2*a6*b23
18
b38=----------------
2
a8
5 2 25 2
---*a2 *a7*b23 - ----*a2*a6 *b23
3 36
b37=----------------------------------
2
a6*a8
5 2 5 2
---*a2 *a7*b23 - ----*a2*a6 *b23
9 36
b36=----------------------------------
2
a6*a8
5
- ----*a6*b23
12
b35=----------------
a8
5 5 2
- ---*a2*a7*b23 - ----*a6 *b23
3 12
b34=---------------------------------
a6*a8
10 5 2
- ----*a2*a7*b23 + ----*a6 *b23
3 12
b33=----------------------------------
a6*a8
5
- ---*a2*a7*b23
2
b32=------------------
a6*a8
10
- ----*a2*a7*b23
3
b31=-------------------
a6*a8
5 5 2
- ---*a2*a7*b23 + ----*a6 *b23
3 12
b30=---------------------------------
a6*a8
5 2
----*a2 *b23
18
b29=--------------
2
a8
5 2
---*a2 *b23
9
b28=-------------
2
a8
5
- ---*a2*b23
3
b27=---------------
a8
10
- ----*a2*b23
3
b26=----------------
a8
5
- ---*a2*b23
2
b25=---------------
a8
5
- ---*a2*b23
6
b24=---------------
a8
5 2 5 2
- ---*a2*a7 *b23 + ----*a6 *a7*b23
9 36
b22=-------------------------------------
2
a6*a8
10 5 2
- ----*a2*a7*b23 + ----*a6 *b23
9 36
b21=----------------------------------
2
a8
5 2 2 5 2 5 4
- ----*a2 *a7 *b23 - ----*a2*a6 *a7*b23 + -----*a6 *b23
18 36 288
b20=----------------------------------------------------------
2 2
a6 *a8
5 2
5*a2*a7*b23 - ---*a6 *b23
8
b19=---------------------------
a2*a8
5 5 2
---*a2*a7*b23 - ----*a6 *b23
4 48
b18=------------------------------
a2*a8
10 2 2 2 5 4
- ----*a2 *a7 *b23 + 5*a2*a6 *a7*b23 - ---*a6 *b23
3 8
b17=-----------------------------------------------------
2
a2*a6 *a8
5 2 2 10 2 5 4
- ---*a2 *a7 *b23 + ----*a2*a6 *a7*b23 - ----*a6 *b23
3 3 16
b16=--------------------------------------------------------
2
a2*a6 *a8
5
- ---*a2*a6*b23
9
b15=------------------
2
a8
5 2 5 2
- ---*a2 *a7*b23 - ----*a2*a6 *b23
9 12
b14=-------------------------------------
2
a6*a8
5
---*a6*b23
4
b13=------------
a8
5 25 2
- ---*a2*a7*b23 + ----*a6 *b23
3 12
b12=---------------------------------
a6*a8
5 5 2
---*a2*a7*b23 + ---*a6 *b23
3 3
b11=-----------------------------
a6*a8
5 5 2
- ---*a2*a7*b23 + ---*a6 *b23
6 4
b10=--------------------------------
a6*a8
5 5 2
---*a2*a7*b23 + ---*a6 *b23
3 4
b9=-----------------------------
a6*a8
5 5 2
---*a2*a7*b23 + ----*a6 *b23
6 24
b8=------------------------------
a6*a8
5
- ---*a6*b23
8
b7=---------------
a2
5 15 2
---*a2*a7*b23 - ----*a6 *b23
2 8
b6=------------------------------
a2*a6
5 5 2
---*a2*a7*b23 - ---*a6 *b23
2 2
b5=-----------------------------
a2*a6
5 2
- ---*a2 *b23
6
b4=----------------
2
a8
5
---*a2*b23
3
b3=------------
a8
5
---*a2*b23
6
b2=------------
a8
1
b1= - ---*b23
4
1
a12= - ---*a6
2
1 2
- a2*a7 + ---*a6
4
a11=--------------------
a6
a10= - a2
a9= - a2
a6=a6
1 2
a2*a7 + ---*a6
4
a5=-----------------
a6
3
- ---*a6*a8
4
a4=--------------
a2
9 2
3*a2*a7*a8 - ---*a6 *a8
4
a3=-------------------------
a2*a6
1
a1= - ---*a8
2
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,a7,a6,a8
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
1 2 1 2
df(u,t)=( - ---*u *a2*a6*a8 + u *f(v,v)*a2 *a7 + ---*u *f(v,v)*a2*a6
2 3x x 4 x
2 9 2
+ u *a2 *a6*u + 3*f(v ,v )*a2*a7*a8 - ---*f(v ,v )*a6 *a8
x x 2x 4 x 2x
3 2 2
- ---*f(v,v )*a6 *a8 + f(v,v )*f(v,v)*a2*a6*a7 + f(v,v )*a2*a6 *u)/(
4 3x x x
a2*a6)
1 2
df(v,t)=( - u *a2*a6*v + v *a6*a8 - v *f(v,v)*a2*a7 + ---*v *f(v,v)*a6
x 3x x 4 x
1 2
- v *a2*a6*u - ---*f(v,v )*a6 *v)/a6
x 2 x
1 2 2 5 2
df(u,s)=( - ---*u *a2*a6 *a8 *b23 + ---*u *f(v,v)*a2 *a6*a7*a8*b23
4 5x 6 3x
5 3 5 2 2
+ ----*u *f(v,v)*a2*a6 *a8*b23 + ---*u *a2 *a6 *a8*b23*u
24 3x 6 3x
5 2 2 5 2
+ ---*u *u *a2 *a6 *a8*b23 + ---*u *f(v,v )*a2 *a6*a7*a8*b23
3 2x x 3 2x x
5 3 5 2
+ ---*u *f(v,v )*a2*a6 *a8*b23 - ---*u *f(v ,v )*a2 *a6*a7*a8*b23
4 2x x 6 x x x
5 3 5 2
+ ---*u *f(v ,v )*a2*a6 *a8*b23 + ---*u *f(v,v )*a2 *a6*a7*a8*b23
4 x x x 3 x 2x
5 3 5 2 3 2
+ ---*u *f(v,v )*a2*a6 *a8*b23 - ----*u *f(v,v) *a2 *a7 *b23
3 x 2x 18 x
5 2 2 2 5 2 4
- ----*u *f(v,v) *a2 *a6 *a7*b23 + -----*u *f(v,v) *a2*a6 *b23
36 x 288 x
5 3 5 2 3
- ---*u *f(v,v)*a2 *a6*a7*b23*u - ----*u *f(v,v)*a2 *a6 *b23*u
9 x 12 x
5 3 2 2 5 2
- ---*u *a2 *a6 *b23*u + ---*f(v ,v )*a2*a6*a7*a8 *b23
6 x 2 2x 3x
5 3 2 5 2
- ---*f(v ,v )*a6 *a8 *b23 + ---*f(v ,v )*a2*a6*a7*a8 *b23
2 2x 3x 2 x 4x
15 3 2 5 2 2
- ----*f(v ,v )*a6 *a8 *b23 - ---*f(v ,v )*f(v,v)*a2 *a7 *a8*b23
8 x 4x 3 x 2x
10 2
+ ----*f(v ,v )*f(v,v)*a2*a6 *a7*a8*b23
3 x 2x
5 4 5 2
- ----*f(v ,v )*f(v,v)*a6 *a8*b23 - ---*f(v ,v )*a2 *a6*a7*a8*b23*u
16 x 2x 3 x 2x
25 3
+ ----*f(v ,v )*a2*a6 *a8*b23*u
12 x 2x
10 2 2
- ----*f(v ,v )*f(v,v )*a2 *a7 *a8*b23
3 x x x
2
+ 5*f(v ,v )*f(v,v )*a2*a6 *a7*a8*b23
x x x
5 4 5 3 2
- ---*f(v ,v )*f(v,v )*a6 *a8*b23 - ---*f(v,v )*a6 *a8 *b23
8 x x x 8 5x
5 2
+ ---*f(v,v )*f(v,v)*a2*a6 *a7*a8*b23
4 3x
5 4 5 3
- ----*f(v,v )*f(v,v)*a6 *a8*b23 + ---*f(v,v )*a2*a6 *a8*b23*u
48 3x 4 3x
2
+ 5*f(v,v )*f(v,v )*a2*a6 *a7*a8*b23
2x x
5 4 5 2 2 2
- ---*f(v,v )*f(v,v )*a6 *a8*b23 - ---*f(v,v )*f(v,v) *a2 *a6*a7 *b23
8 2x x 9 x
5 2 3
+ ----*f(v,v )*f(v,v) *a2*a6 *a7*b23
36 x
10 2 2
- ----*f(v,v )*f(v,v)*a2 *a6 *a7*b23*u
9 x
5 4 5 2 3 2
+ ----*f(v,v )*f(v,v)*a2*a6 *b23*u - ---*f(v,v )*a2 *a6 *b23*u )/(a2
36 x 9 x
2 2
*a6 *a8 )
5 2 5 2
df(v,s)=( - ---*u *a2*a6 *a8*b23*v - ---*u *v *a2*a6 *a8*b23
6 3x 2 2x x
10 2 5 2
- ----*u *v *a2*a6 *a8*b23 + ---*u *f(v,v)*a2 *a6*a7*b23*v
3 x 2x 9 x
5 3 5 2 2
- ----*u *f(v,v)*a2*a6 *b23*v + ---*u *a2 *a6 *b23*u*v
36 x 9 x
2 2 5
+ v *a6 *a8 *b23 - ---*v *f(v,v)*a2*a6*a7*a8*b23
5x 3 3x
5 3 5 2
+ ----*v *f(v,v)*a6 *a8*b23 - ---*v *a2*a6 *a8*b23*u
12 3x 3 3x
10 5
- ----*v *f(v,v )*a2*a6*a7*a8*b23 - ---*v *f(v ,v )*a2*a6*a7*a8*b23
3 2x x 2 x x x
10 5 3
- ----*v *f(v,v )*a2*a6*a7*a8*b23 + ----*v *f(v,v )*a6 *a8*b23
3 x 2x 12 x 2x
5 2 2 2 5 2 2
+ ---*v *f(v,v) *a2 *a7 *b23 - ----*v *f(v,v) *a2*a6 *a7*b23
6 x 12 x
5 2 4 5 2
+ -----*v *f(v,v) *a6 *b23 + ---*v *f(v,v)*a2 *a6*a7*b23*u
288 x 3 x
25 3 5 2 2 2
- ----*v *f(v,v)*a2*a6 *b23*u + ----*v *a2 *a6 *b23*u
36 x 18 x
5 5 3
- ---*f(v ,v )*a2*a6*a7*a8*b23*v - ----*f(v ,v )*a6 *a8*b23*v
3 x 2x 12 x 2x
5 3 5 2
- ----*f(v,v )*a6 *a8*b23*v + ----*f(v,v )*f(v,v)*a2*a6 *a7*b23*v
12 3x 18 x
5 4 5 3 2
- ----*f(v,v )*f(v,v)*a6 *b23*v + ----*f(v,v )*a2*a6 *b23*u*v)/(a6
72 x 18 x
2
*a8 )