Solution 18 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2 3 1 3
-----*a1 *a18 *b1 + ---*a13 *a18*a9*b1
128 8
b42=----------------------------------------
2 3
a1 *a13
7 2 2 3
----*a1 *a18 *b1 - a13 *a9*b1
16
b41=-------------------------------
3
a1 *a13
1 2 2 3
- ----*a1 *a18 *b1 + a13 *a9*b1
16
b40=----------------------------------
2 2
a1 *a13
b39=0
- 6*a13*a18*b1
b38=-----------------
2
a1
3*a18*b1
b37=----------
a1
b36=0
3
---*a18*b1
2
b35=------------
a1
1
- ---*a18*b1
4
b34=---------------
a13
1
- ---*a18*b1
4
b33=---------------
a13
b32=0
b31=0
3
16*a13 *b1
b30=------------
3
a1
b29=0
2
- 12*a13 *b1
b28=---------------
2
a1
b27=0
b26=0
a13*b1
b25=--------
a1
b24=0
1 2 4 1 3 2
-----*a1 *a18 *b1 + ----*a13 *a18 *a9*b1
512 32
b23=------------------------------------------
5
a1*a13
7 2 3 1 3
----*a1 *a18 *b1 - ---*a13 *a18*a9*b1
64 4
b22=---------------------------------------
2 3
a1 *a13
1 2 3 3
----*a1 *a18 *b1 + a13 *a18*a9*b1
32
b21=-----------------------------------
4
a1*a13
3 2
- ---*a18 *b1
2
b20=----------------
a1*a13
5 2 2 3
---*a1 *a18 *b1 - 4*a13 *a9*b1
2
b19=--------------------------------
2 2
a1 *a13
13 2 2 3
----*a1 *a18 *b1 - a13 *a9*b1
16
b18=-------------------------------
2 2
a1 *a13
1 2 2 3
- ---*a1 *a18 *b1 + 2*a13 *a9*b1
8
b17=-----------------------------------
3
a1*a13
1 2 2 3
- ---*a1 *a18 *b1 + a13 *a9*b1
8
b16=---------------------------------
3
a1*a13
1 2 2 3
- ---*a1 *a18 *b1 + a13 *a9*b1
8
b15=---------------------------------
3
a1*a13
4*a13*a18*b1
b14=--------------
2
a1
- 12*a18*b1
b13=--------------
a1
- 15*a18*b1
b12=--------------
a1
3*a18*b1
b11=----------
a13
3*a18*b1
b10=----------
a13
6*a18*b1
b9=----------
a13
7
---*a18*b1
4
b8=------------
a13
1
- ---*a1*a18*b1
4
b7=------------------
2
a13
3
- ---*a1*a18*b1
4
b6=------------------
2
a13
b5=0
2
48*a13 *b1
b4=------------
2
a1
- 12*a13*b1
b3=--------------
a1
- 12*a13*b1
b2=--------------
a1
1 2 2 1 3
----*a1 *a18 + ---*a13 *a9
64 4
a19=-----------------------------
2
a1*a13
1
- ---*a1*a18
4
a17=---------------
a13
a16=0
2
- 4*a13
a15=-----------
a1
a14=0
a12=0
1 2 3 1 3
-----*a1 *a18 + ----*a13 *a18*a9
256 16
a11=-----------------------------------
4
a13
1 2
---*a1*a18
4
a10=-------------
2
a13
a8= - a18
2*a1*a18
a7=----------
a13
5
---*a1*a18
4
a6=------------
a13
1 2
- ---*a1 *a18
4
a5=----------------
2
a13
1 2
- ---*a1 *a18
4
a4=----------------
2
a13
a3=0
a2= - 8*a13
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,a9,a13,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
4 5 3 5
df(u,t)=(u *a1*a13 + ---*u *f(v,v)*a1*a13 *a18 - 8*u *a13 *u
2x 4 x x
1 2 2 1 2 2
- ---*f(v ,v )*a1 *a13 *a18 - ---*f(v,v )*a1 *a13 *a18
4 x x 4 2x
4 3
+ f(v,v )*f(v,v)*a13 *a9 + 2*f(v,v )*a1*a13 *a18*u
x x
1 3 2 3 1 3 3
+ -----*f(v,v) *a1 *a18 + ----*f(v,v) *a13 *a18*a9
256 16
1 2 2 2 4 2 4
+ ---*f(v,v) *a1*a13 *a18 *u - f(v,v)*a13 *a18*u )/a13
4
3 1 2 1 2 2 2
df(v,t)=(u *a1*a13 *v - ---*f(v,v )*a1 *a13*a18*v + ----*f(v,v) *a1 *a18 *v
x 4 x 64
1 2 3 2 4 2
+ ---*f(v,v) *a13 *a9*v + f(v,v)*a1*a13 *a18*u*v - 4*a13 *u *v)/(a1
4
2
*a13 )
2 5 7 2 4 6
df(u,s)=(u *a1 *a13 *b1 + ---*u *f(v,v)*a1 *a13 *a18*b1 - 12*u *a1*a13 *b1*u
3x 4 2x 2x
2 6 2 4
- 12*u *a1*a13 *b1 + 6*u *f(v,v )*a1 *a13 *a18*b1
x x x
13 2 2 3 2 2 6
+ ----*u *f(v,v) *a1 *a13 *a18 *b1 - u *f(v,v) *a13 *a9*b1
16 x x
5 7 2
- 15*u *f(v,v)*a1*a13 *a18*b1*u + 48*u *a13 *b1*u
x x
3 3 3 1 3 2 2
- ---*f(v ,v )*a1 *a13 *a18*b1 - ---*f(v ,v )*f(v,v)*a1 *a13 *a18 *b1
4 x 2x 8 x x
5 2 4
+ f(v ,v )*f(v,v)*a1*a13 *a9*b1 + 3*f(v ,v )*a1 *a13 *a18*b1*u
x x x x
1 3 3 1 3 2 2
- ---*f(v,v )*a1 *a13 *a18*b1 - ---*f(v,v )*f(v,v)*a1 *a13 *a18 *b1
4 3x 8 2x
5 2 4
+ f(v,v )*f(v,v)*a1*a13 *a9*b1 + 3*f(v,v )*a1 *a13 *a18*b1*u
2x 2x
1 2 3 2 2 2 5
- ---*f(v,v ) *a1 *a13 *a18 *b1 + 2*f(v,v ) *a1*a13 *a9*b1
8 x x
1 2 3 3
+ ----*f(v,v )*f(v,v) *a1 *a13*a18 *b1
32 x
2 4
+ f(v,v )*f(v,v) *a1*a13 *a18*a9*b1
x
5 2 3 2
+ ---*f(v,v )*f(v,v)*a1 *a13 *a18 *b1*u
2 x
6 5 2
- 4*f(v,v )*f(v,v)*a13 *a9*b1*u - 12*f(v,v )*a1*a13 *a18*b1*u
x x
1 4 3 4 1 4 3 2
+ -----*f(v,v) *a1 *a18 *b1 + ----*f(v,v) *a1*a13 *a18 *a9*b1
512 32
7 3 2 2 3 1 3 5
+ ----*f(v,v) *a1 *a13 *a18 *b1*u - ---*f(v,v) *a13 *a18*a9*b1*u
64 4
3 2 4 2 2 6 3 2 5
- ---*f(v,v) *a1*a13 *a18 *b1*u + 4*f(v,v)*a13 *a18*b1*u )/(a1 *a13 )
2
2 4 3 2 3
df(v,s)=(u *a1 *a13 *b1*v + ---*u *f(v,v)*a1 *a13 *a18*b1*v
2x 2 x
5 1 3 2
- 12*u *a1*a13 *b1*u*v - ---*f(v ,v )*a1 *a13 *a18*b1*v
x 4 x x
1 3 2
- ---*f(v,v )*a1 *a13 *a18*b1*v
4 2x
1 3 2
- ----*f(v,v )*f(v,v)*a1 *a13*a18 *b1*v
16 x
4 2 3
+ f(v,v )*f(v,v)*a1*a13 *a9*b1*v + 3*f(v,v )*a1 *a13 *a18*b1*u*v
x x
1 3 3 3 1 3 3
+ -----*f(v,v) *a1 *a18 *b1*v + ---*f(v,v) *a1*a13 *a18*a9*b1*v
128 8
7 2 2 2 2 2 5
+ ----*f(v,v) *a1 *a13 *a18 *b1*u*v - f(v,v) *a13 *a9*b1*u*v
16
4 2 6 3 3 3
- 6*f(v,v)*a1*a13 *a18*b1*u *v + 16*a13 *b1*u *v)/(a1 *a13 )