Solution 10 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2
- a1*a18*a6*b38 + ---*a14*a6 *b38
4
b42=------------------------------------
3
a14
- 2*a1*a18*b38 + a14*a6*b38
b41=------------------------------
2
a14
a1*a6*b38
b40=-----------
2
a14
1 2
- a1*a18*a6*b38 + ---*a14*a6 *b38
4
b39=------------------------------------
2
a14 *a18
b37=0
- 2*a1*a18*b38 + a14*a6*b38
b36=------------------------------
a14*a18
a1*b38
b35=--------
a14
b34=0
b33=0
a1*a6*b38
b32=-----------
a14*a18
b31=0
b30=0
a14*b38
b29=---------
a18
b28=0
b27=0
a1*b38
b26=--------
a18
b25=0
b24=0
2 1 3
a1*a18*a6 *b38 - ---*a14*a6 *b38
4
b23=----------------------------------
4
a14
2
2*a1*a18*a6*b38 - a14*a6 *b38
b22=-------------------------------
3
a14
1 3
---*a6 *b38
2
b21=-------------
2
a14 *a18
- a6*b38
b20=-----------
a14
2
2*a1*a18*a6*b38 + 2*a14*a6 *b38
b19=---------------------------------
2
a14 *a18
3 2
- a1*a18*a6*b38 + ---*a14*a6 *b38
4
b18=------------------------------------
2
a14 *a18
2
2*a1*a6 *b38
b17=--------------
2
a14 *a18
3 2
---*a1*a6 *b38
2
b16=----------------
2
a14 *a18
3 2
---*a1*a6 *b38
2
b15=----------------
2
a14 *a18
b14=0
2*a6*b38
b13=----------
a18
3*a6*b38
b12=----------
a18
3*a1*a6*b38
b11=-------------
a14*a18
3*a1*a6*b38
b10=-------------
a14*a18
5*a1*a6*b38
b9=-------------
a14*a18
3
---*a1*a6*b38
2
b8=---------------
a14*a18
2
a1 *a6*b38
b7=------------
2
a14 *a18
2
3*a1 *a6*b38
b6=--------------
2
a14 *a18
b5=0
3*a14*b38
b4=-----------
a18
3*a1*b38
b3=----------
a18
3*a1*b38
b2=----------
a18
2
a1 *b38
b1=---------
a14*a18
2 1
- 2*a1*a18 + ---*a14*a18*a6
2
a19=-------------------------------
2
a14
a17=0
1
- 2*a1*a18 + ---*a14*a6
2
a16=--------------------------
a14
a15=0
a13=0
a12=0
2 1 2
2*a1*a18 *a6 - ---*a14*a18*a6
2
a11=--------------------------------
3
a14
- a18*a6
a10=-----------
a14
1 2
2*a1*a18*a6 + ---*a14*a6
2
a9=---------------------------
2
a14
a8=0
a7=a6
a1*a6
a5=-------
a14
a1*a6
a4=-------
a14
a3=0
a2=2*a14
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,a6,a14,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 3 4 2
df(u,t)=(u *a1*a14 + u *f(v,v)*a14 *a6 + 2*u *a14 *u + f(v ,v )*a1*a14 *a6
2x x x x x
2
+ f(v,v )*a1*a14 *a6 + 2*f(v,v )*f(v,v)*a1*a14*a18*a6
2x x
1 2 2 3
+ ---*f(v,v )*f(v,v)*a14 *a6 + f(v,v )*a14 *a6*u
2 x x
3 2 1 3 2
+ 2*f(v,v) *a1*a18 *a6 - ---*f(v,v) *a14*a18*a6
2
2 2 3
- f(v,v) *a14 *a18*a6*u)/a14
1 2 3
df(v,t)=( - 2*v *f(v,v)*a1*a14*a18 + ---*v *f(v,v)*a14 *a6 + v *a14 *u
x 2 x x
2 2 1 2 2
- 2*f(v,v) *a1*a18 *v + ---*f(v,v) *a14*a18*a6*v + f(v,v)*a14 *a18*u*v
2
2
)/a14
2 3 3 3 4
df(u,s)=(u *a1 *a14 *b38 + ---*u *f(v,v)*a1*a14 *a6*b38 + 3*u *a1*a14 *b38*u
3x 2 2x 2x
2 4 3
+ 3*u *a1*a14 *b38 + 5*u *f(v,v )*a1*a14 *a6*b38
x x x
2 2 3 2 3 2
- u *f(v,v) *a1*a14 *a18*a6*b38 + ---*u *f(v,v) *a14 *a6 *b38
x 4 x
4 5 2
+ 3*u *f(v,v)*a14 *a6*b38*u + 3*u *a14 *b38*u
x x
2 2 3 2 2
+ 3*f(v ,v )*a1 *a14 *a6*b38 + ---*f(v ,v )*f(v,v)*a1*a14 *a6 *b38
x 2x 2 x x
3 2 2
+ 3*f(v ,v )*a1*a14 *a6*b38*u + f(v,v )*a1 *a14 *a6*b38
x x 3x
3 2 2 3
+ ---*f(v,v )*f(v,v)*a1*a14 *a6 *b38 + 3*f(v,v )*a1*a14 *a6*b38*u
2 2x 2x
2 2 2 1 2 2 3
+ 2*f(v,v ) *a1*a14 *a6 *b38 + ---*f(v,v )*f(v,v) *a14 *a6 *b38
x 2 x
2
+ 2*f(v,v )*f(v,v)*a1*a14 *a18*a6*b38*u
x
3 2 4 2
+ 2*f(v,v )*f(v,v)*a14 *a6 *b38*u + 2*f(v,v )*a14 *a6*b38*u
x x
4 2 2 1 4 3
+ f(v,v) *a1*a18 *a6 *b38 - ---*f(v,v) *a14*a18*a6 *b38
4
3 2 3 2 2
+ 2*f(v,v) *a1*a14*a18 *a6*b38*u - f(v,v) *a14 *a18*a6 *b38*u
2 3 2 4
- f(v,v) *a14 *a18*a6*b38*u )/(a14 *a18)
3 2
df(v,s)=(u *v *a1*a14 *b38 + u *f(v,v)*a1*a14 *a18*b38*v
x x x
2 2
+ v *f(v,v )*a1*a14 *a6*b38 - v *f(v,v) *a1*a14*a18*a6*b38
x x x
1 2 2 2 2
+ ---*v *f(v,v) *a14 *a6 *b38 - 2*v *f(v,v)*a1*a14 *a18*b38*u
4 x x
3 4 2
+ v *f(v,v)*a14 *a6*b38*u + v *a14 *b38*u
x x
3 2
+ f(v,v )*f(v,v)*a1*a14*a18*a6*b38*v - f(v,v) *a1*a18 *a6*b38*v
x
1 3 2 2 2
+ ---*f(v,v) *a14*a18*a6 *b38*v - 2*f(v,v) *a1*a14*a18 *b38*u*v
4
2 2 3 2 3
+ f(v,v) *a14 *a18*a6*b38*u*v + f(v,v)*a14 *a18*b38*u *v)/(a14 *a18)