Solution 13 to problem l112o23
Expressions |
Parameters |
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Back to problem l112o23
Expressions
The solution is given through the following expressions:
1 2
---*a4 *b38
4
b42=-------------
2
a1
a4*b38
b41=--------
a1
a4*b38
b40=--------
a14
1 2
---*a14*a4 *b38
4
b39=-----------------
2
a1 *a18
b37=0
a14*a4*b38
b36=------------
a1*a18
a1*b38
b35=--------
a14
b34=0
b33=0
a4*b38
b32=--------
a18
b31=0
b30=0
a14*b38
b29=---------
a18
b28=0
b27=0
a1*b38
b26=--------
a18
b25=0
b24=0
1 3
- ---*a4 *b38
4
b23=----------------
3
a1
2
- a4 *b38
b22=------------
2
a1
2 2 1 2 3
- a1 *a18*a4 *b38 + ---*a14 *a4 *b38
2
b21=---------------------------------------
3
a1 *a14*a18
- a4*b38
b20=-----------
a1
2
2*a14*a4 *b38
b19=---------------
2
a1 *a18
2 3 2 2
- a1 *a18*a4*b38 + ---*a14 *a4 *b38
4
b18=--------------------------------------
2
a1 *a14*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
2*a14*a4*b38
b13=--------------
a1*a18
3*a14*a4*b38
b12=--------------
a1*a18
3*a4*b38
b11=----------
a18
3*a4*b38
b10=----------
a18
5*a4*b38
b9=----------
a18
3
---*a4*b38
2
b8=------------
a18
a1*a4*b38
b7=-----------
a14*a18
3*a1*a4*b38
b6=-------------
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
1
---*a18*a4
2
a19=------------
a1
a17=0
1
---*a14*a4
2
a16=------------
a1
a15=0
a13=0
a12=0
1 2
- ---*a18*a4
2
a11=----------------
2
a1
- a18*a4
a10=-----------
a1
1 2
---*a14*a4
2
a9=-------------
2
a1
a8=0
a14*a4
a7=--------
a1
a14*a4
a6=--------
a1
a5=a4
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,a4,a14,a18,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 2
df(u,t)=(u *a1 + u *f(v,v)*a1*a14*a4 + 2*u *a1 *a14*u + f(v ,v )*a1 *a4
2x x x x x
2 1 2
+ f(v,v )*a1 *a4 + ---*f(v,v )*f(v,v)*a14*a4 + f(v,v )*a1*a14*a4*u
2x 2 x x
1 3 2 2 2
- ---*f(v,v) *a18*a4 - f(v,v) *a1*a18*a4*u)/a1
2
df(v,t)=
1 1 2
---*v *f(v,v)*a14*a4 + v *a1*a14*u + ---*f(v,v) *a18*a4*v + f(v,v)*a1*a18*u*v
2 x x 2
-------------------------------------------------------------------------------
a1
5 3 3 4
df(u,s)=(u *a1 *b38 + ---*u *f(v,v)*a1 *a14*a4*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*a4*b38
x x x
2 3 3 2 2 2
- u *f(v,v) *a1 *a18*a4*b38 + ---*u *f(v,v) *a1*a14 *a4 *b38
x 4 x
2 2 3 2 2
+ 3*u *f(v,v)*a1 *a14 *a4*b38*u + 3*u *a1 *a14 *b38*u
x x
4 3 2 2
+ 3*f(v ,v )*a1 *a4*b38 + ---*f(v ,v )*f(v,v)*a1 *a14*a4 *b38
x 2x 2 x x
3 4
+ 3*f(v ,v )*a1 *a14*a4*b38*u + f(v,v )*a1 *a4*b38
x x 3x
3 2 2 3
+ ---*f(v,v )*f(v,v)*a1 *a14*a4 *b38 + 3*f(v,v )*a1 *a14*a4*b38*u
2 2x 2x
2 2 2 2 2 2
+ 2*f(v,v ) *a1 *a14*a4 *b38 - f(v,v )*f(v,v) *a1 *a18*a4 *b38
x x
1 2 2 3
+ ---*f(v,v )*f(v,v) *a14 *a4 *b38
2 x
2 2 2 2 2
+ 2*f(v,v )*f(v,v)*a1*a14 *a4 *b38*u + 2*f(v,v )*a1 *a14 *a4*b38*u
x x
1 4 3 3 2
- ---*f(v,v) *a14*a18*a4 *b38 - f(v,v) *a1*a14*a18*a4 *b38*u
4
2 2 2 3
- f(v,v) *a1 *a14*a18*a4*b38*u )/(a1 *a14*a18)
3 3 2
df(v,s)=(u *v *a1 *a14*b38 + u *f(v,v)*a1 *a18*b38*v + v *f(v,v )*a1 *a14*a4*b38
x x x x x
1 2 2 2 2
+ ---*v *f(v,v) *a14 *a4 *b38 + v *f(v,v)*a1*a14 *a4*b38*u
4 x x
2 2 2 2
+ v *a1 *a14 *b38*u + f(v,v )*f(v,v)*a1 *a18*a4*b38*v
x x
1 3 2 2
+ ---*f(v,v) *a14*a18*a4 *b38*v + f(v,v) *a1*a14*a18*a4*b38*u*v
4
2 2 2
+ f(v,v)*a1 *a14*a18*b38*u *v)/(a1 *a14*a18)