Solution 29 to problem l112o23
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
b42=0
b41=0
b40=0
2 1 1 2
a16 *b1 - ---*a16*a6*b1 + ---*a6 *b1
2 4
b39=--------------------------------------
2
a1
b38=0
b37=0
1
a14*a16*b1 + ---*a14*a6*b1
2
b36=----------------------------
2
a1
b35=0
b34=0
b33=0
a14*a4*b1
b32=-----------
2
a1
b31=0
b30=0
2
a14 *b1
b29=---------
2
a1
b28=0
b27=0
a14*b1
b26=--------
a1
b25=0
b24=0
b23=0
b22=0
2 1 2 1 3
- a16 *a6*b1 + ---*a16*a6 *b1 + ---*a6 *b1
2 2
b21=---------------------------------------------
2
a1 *a14
b20=0
5 2
- a16*a6*b1 + ---*a6 *b1
2
b19=---------------------------
2
a1
3 2
---*a6 *b1
4
b18=------------
2
a1
2
- 2*a1*a16*a6*b1 + 2*a1*a6 *b1 + 2*a14*a16*a4*b1
b17=---------------------------------------------------
2
a1 *a14
2 1
- a1*a16*a6*b1 + a1*a6 *b1 + a14*a16*a4*b1 + ---*a14*a4*a6*b1
2
b16=----------------------------------------------------------------
2
a1 *a14
2 1
- a1*a16*a6*b1 + a1*a6 *b1 + a14*a16*a4*b1 + ---*a14*a4*a6*b1
2
b15=----------------------------------------------------------------
2
a1 *a14
b14=0
2*a14*a6*b1
b13=-------------
2
a1
3*a14*a6*b1
b12=-------------
2
a1
a1*a6*b1 + 2*a14*a4*b1
b11=------------------------
2
a1
a1*a6*b1 + 2*a14*a4*b1
b10=------------------------
2
a1
3*a1*a6*b1 + 2*a14*a4*b1
b9=--------------------------
2
a1
3
---*a6*b1
2
b8=-----------
a1
a4*b1
b7=-------
a1
3*a4*b1
b6=---------
a1
b5=0
2
3*a14 *b1
b4=-----------
2
a1
3*a14*b1
b3=----------
a1
3*a14*b1
b2=----------
a1
a19=0
a18=0
a17=0
a15=0
a13=0
a12=0
a11=0
a10=0
2
- a16*a6 + a6
a9=-----------------
a14
a8=0
a7=a6
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:
b1,a16,a6,a4,a14,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=(u *a1*a14 + u *f(v,v)*a14*a6 + 2*u *a14 *u + f(v ,v )*a14*a4
2x x x x x
2
+ f(v,v )*a14*a4 - f(v,v )*f(v,v)*a16*a6 + f(v,v )*f(v,v)*a6
2x x x
+ f(v,v )*a14*a6*u)/a14
x
df(v,t)=v *f(v,v)*a16 + v *a14*u
x x
2 3 2
df(u,s)=(u *a1 *a14*b1 + ---*u *f(v,v)*a1*a14*a6*b1 + 3*u *a1*a14 *b1*u
3x 2 2x 2x
2 2
+ 3*u *a1*a14 *b1 + 3*u *f(v,v )*a1*a14*a6*b1
x x x
2 3 2 2
+ 2*u *f(v,v )*a14 *a4*b1 + ---*u *f(v,v) *a14*a6 *b1
x x 4 x
2 3 2
+ 3*u *f(v,v)*a14 *a6*b1*u + 3*u *a14 *b1*u
x x
+ 3*f(v ,v )*a1*a14*a4*b1 - f(v ,v )*f(v,v)*a1*a16*a6*b1
x 2x x x
2
+ f(v ,v )*f(v,v)*a1*a6 *b1 + f(v ,v )*f(v,v)*a14*a16*a4*b1
x x x x
1
+ ---*f(v ,v )*f(v,v)*a14*a4*a6*b1 + f(v ,v )*a1*a14*a6*b1*u
2 x x x x
2
+ 2*f(v ,v )*a14 *a4*b1*u + f(v,v )*a1*a14*a4*b1
x x 3x
2
- f(v,v )*f(v,v)*a1*a16*a6*b1 + f(v,v )*f(v,v)*a1*a6 *b1
2x 2x
1
+ f(v,v )*f(v,v)*a14*a16*a4*b1 + ---*f(v,v )*f(v,v)*a14*a4*a6*b1
2x 2 2x
2
+ f(v,v )*a1*a14*a6*b1*u + 2*f(v,v )*a14 *a4*b1*u
2x 2x
2 2 2
- 2*f(v,v ) *a1*a16*a6*b1 + 2*f(v,v ) *a1*a6 *b1
x x
2 2 2
+ 2*f(v,v ) *a14*a16*a4*b1 - f(v,v )*f(v,v) *a16 *a6*b1
x x
1 2 2 1 2 3
+ ---*f(v,v )*f(v,v) *a16*a6 *b1 + ---*f(v,v )*f(v,v) *a6 *b1
2 x 2 x
5 2
- f(v,v )*f(v,v)*a14*a16*a6*b1*u + ---*f(v,v )*f(v,v)*a14*a6 *b1*u
x 2 x
2 2 2
+ 2*f(v,v )*a14 *a6*b1*u )/(a1 *a14)
x
2 2
df(v,s)=(u *v *a1*a14*b1 + v *f(v,v )*a14*a4*b1 + v *f(v,v) *a16 *b1
x x x x x
1 2 1 2 2
- ---*v *f(v,v) *a16*a6*b1 + ---*v *f(v,v) *a6 *b1
2 x 4 x
1 2 2
+ v *f(v,v)*a14*a16*b1*u + ---*v *f(v,v)*a14*a6*b1*u + v *a14 *b1*u )/
x 2 x x
2
a1