Solution 9 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2 1 2
- ---*a17 *a4*b38 + ---*a18*a4 *b38
4 4
b42=--------------------------------------
2
a1 *a18
1 2
- ---*a17 *b38 + a18*a4*b38
2
b41=------------------------------
a1*a18
b40=0
1 2
- ---*a4 *b38
2
b39=----------------
a1*a17
a17*b38
b37=---------
a18
- 2*a4*b38
b36=-------------
a17
1
- ---*a17*b38
2
b35=----------------
a18
b34=0
b33=0
a4*b38
b32=--------
a18
b31=0
b30=0
- 2*a1*b38
b29=-------------
a17
b28=0
b27=0
a1*b38
b26=--------
a18
b25=0
b24=0
1 2 2 1 3
---*a17 *a4 *b38 - ---*a18*a4 *b38
4 4
b23=------------------------------------
3
a1 *a18
1 2 2
---*a17 *a4*b38 - a18*a4 *b38
2
b22=-------------------------------
2
a1 *a18
3
- a4 *b38
b21=------------
2
a1 *a17
- a4*b38
b20=-----------
a1
2 2
- a17 *a4*b38 - 4*a18*a4 *b38
b19=--------------------------------
a1*a17*a18
1 2 3 2
---*a17 *a4*b38 - ---*a18*a4 *b38
2 2
b18=-----------------------------------
a1*a17*a18
2
2*a4 *b38
b17=-----------
a1*a18
3 2
---*a4 *b38
2
b16=-------------
a1*a18
3 2
---*a4 *b38
2
b15=-------------
a1*a18
b14=0
- 4*a4*b38
b13=-------------
a17
- 6*a4*b38
b12=-------------
a17
3*a4*b38
b11=----------
a18
3*a4*b38
b10=----------
a18
5*a4*b38
b9=----------
a18
3
---*a4*b38
2
b8=------------
a18
1
- ---*a17*a4*b38
2
b7=-------------------
2
a18
3
- ---*a17*a4*b38
2
b6=-------------------
2
a18
b5=0
- 6*a1*b38
b4=-------------
a17
3*a1*b38
b3=----------
a18
3*a1*b38
b2=----------
a18
1
- ---*a1*a17*b38
2
b1=-------------------
2
a18
1 2 1
- ---*a17 + ---*a18*a4
2 2
a19=--------------------------
a1
- a18*a4
a16=-----------
a17
a15=0
- 2*a1*a18
a14=-------------
a17
a13=0
a12=0
1 2 1 2
---*a17 *a4 - ---*a18*a4
2 2
a11=---------------------------
2
a1
- a18*a4
a10=-----------
a1
2 2
- a17 *a4 - a18*a4
a9=----------------------
a1*a17
a8=0
- 2*a18*a4
a7=-------------
a17
- 2*a18*a4
a6=-------------
a17
a5=a4
a3=0
- 4*a1*a18
a2=-------------
a17
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:
b38,a17,a4,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 3
df(u,t)=(u *a1 *a17 - 2*u *f(v,v)*a1 *a18*a4 - 4*u *a1 *a18*u
2x x x
2 2
+ f(v ,v )*a1 *a17*a4 + f(v,v )*a1 *a17*a4
x x 2x
2 2
- f(v,v )*f(v,v)*a1*a17 *a4 - f(v,v )*f(v,v)*a1*a18*a4
x x
2 1 3 3
- 2*f(v,v )*a1 *a18*a4*u + ---*f(v,v) *a17 *a4
x 2
1 3 2 2 2
- ---*f(v,v) *a17*a18*a4 - f(v,v) *a1*a17*a18*a4*u)/(a1 *a17)
2
2 2
df(v,t)=( - v *f(v,v)*a1*a18*a4 - 2*v *a1 *a18*u + f(v,v )*a1*a17 *v
x x x
1 2 3 1 2
- ---*f(v,v) *a17 *v + ---*f(v,v) *a17*a18*a4*v
2 2
+ f(v,v)*a1*a17*a18*u*v)/(a1*a17)
1 4 2 3 3
df(u,s)=( - ---*u *a1 *a17 *b38 + ---*u *f(v,v)*a1 *a17*a18*a4*b38
2 3x 2 2x
4 2 4
+ 3*u *a1 *a17*a18*b38*u + 3*u *a1 *a17*a18*b38
2x x
3 1 2 2 2
+ 5*u *f(v,v )*a1 *a17*a18*a4*b38 + ---*u *f(v,v) *a1 *a17 *a18*a4*b38
x x 2 x
3 2 2 2 2 3 2
- ---*u *f(v,v) *a1 *a18 *a4 *b38 - 6*u *f(v,v)*a1 *a18 *a4*b38*u
2 x x
4 2 2 3 3 2
- 6*u *a1 *a18 *b38*u - ---*f(v ,v )*a1 *a17 *a4*b38
x 2 x 2x
3 2 2
+ ---*f(v ,v )*f(v,v)*a1 *a17*a18*a4 *b38
2 x x
3 1 3 2
+ 3*f(v ,v )*a1 *a17*a18*a4*b38*u - ---*f(v,v )*a1 *a17 *a4*b38
x x 2 3x
3 2 2
+ ---*f(v,v )*f(v,v)*a1 *a17*a18*a4 *b38
2 2x
3 2 2 2
+ 3*f(v,v )*a1 *a17*a18*a4*b38*u + 2*f(v,v ) *a1 *a17*a18*a4 *b38
2x x
2 2 3
- f(v,v )*f(v,v) *a1*a18 *a4 *b38
x
2 2
- f(v,v )*f(v,v)*a1 *a17 *a18*a4*b38*u
x
2 2 2 3 2 2
- 4*f(v,v )*f(v,v)*a1 *a18 *a4 *b38*u - 4*f(v,v )*a1 *a18 *a4*b38*u
x x
1 4 3 2 1 4 2 3
+ ---*f(v,v) *a17 *a18*a4 *b38 - ---*f(v,v) *a17*a18 *a4 *b38
4 4
1 3 3 3 2 2
+ ---*f(v,v) *a1*a17 *a18*a4*b38*u - f(v,v) *a1*a17*a18 *a4 *b38*u
2
2 2 2 2 3 2
- f(v,v) *a1 *a17*a18 *a4*b38*u )/(a1 *a17*a18 )
3 1 2 2
df(v,s)=(u *v *a1 *a17*b38 - ---*u *f(v,v)*a1 *a17 *b38*v
x x 2 x
2 1 2 2
+ v *f(v,v )*a1 *a17*a4*b38 - ---*v *f(v,v) *a1*a18*a4 *b38
x x 2 x
2 3 2
- 2*v *f(v,v)*a1 *a18*a4*b38*u - 2*v *a1 *a18*b38*u
x x
2 2 1 3 3
+ f(v,v )*a1 *a17 *b38*u*v - ---*f(v,v) *a17 *a4*b38*v
x 4
1 3 2 1 2 3
+ ---*f(v,v) *a17*a18*a4 *b38*v - ---*f(v,v) *a1*a17 *b38*u*v
4 2
2 2 2 2
+ f(v,v) *a1*a17*a18*a4*b38*u*v + f(v,v)*a1 *a17*a18*b38*u *v)/(a1
*a17*a18)