Solution 25 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
b42=0
b41=0
2
- a14*a9*b1 + 2*a16 *b1
b40=--------------------------
2
a1
2
a16 *b1
b39=---------
2
a1
b38=0
2 2
- a14 *a9*b1 + 2*a14*a16 *b1
b37=-------------------------------
2
a1 *a16
2*a14*a16*b1
b36=--------------
2
a1
1 2 2
- ---*a14 *a9*b1 + a14*a16 *b1
2
b35=---------------------------------
2
a1 *a16
1 2
- ---*a14*a9*b1 + a16 *b1
2
b34=----------------------------
a1*a16
1 2
- ---*a14*a9*b1 + a16 *b1
2
b33=----------------------------
a1*a16
2*a16*b1
b32=----------
a1
b31=0
b30=0
2
a14 *b1
b29=---------
2
a1
1 3 2 2
- ---*a14 *a9*b1 + a14 *a16 *b1
2
b28=----------------------------------
2 2
a1 *a16
b27=0
a14*b1
b26=--------
a1
1 2 1 2
- ---*a14 *a9*b1 + ---*a14*a16 *b1
4 2
b25=-------------------------------------
2
a1*a16
b24=0
b23=0
b22=0
2*a16*a9*b1
b21=-------------
2
a1
b20=0
2
2*a14*a9*b1 + 4*a16 *b1
b19=-------------------------
2
a1
2
a14*a9*b1 + a16 *b1
b18=---------------------
2
a1
2
8*a16 *b1
b17=-----------
a1*a14
2
a14*a9*b1 + 4*a16 *b1
b16=-----------------------
a1*a14
2
a14*a9*b1 + 4*a16 *b1
b15=-----------------------
a1*a14
b14=0
4*a14*a16*b1
b13=--------------
2
a1
2 2
a14 *a9*b1 + 4*a14*a16 *b1
b12=----------------------------
2
a1 *a16
6*a16*b1
b11=----------
a1
6*a16*b1
b10=----------
a1
10*a16*b1
b9=-----------
a1
1 2
---*a14*a9*b1 + 2*a16 *b1
2
b8=---------------------------
a1*a16
2*a16*b1
b7=----------
a14
6*a16*b1
b6=----------
a14
b5=0
2
3*a14 *b1
b4=-----------
2
a1
3*a14*b1
b3=----------
a1
3*a14*b1
b2=----------
a1
a19=0
a18=0
1 2
- ---*a14*a9 + a16
2
a17=----------------------
a16
a15=0
1 2 1 2
- ---*a14 *a9 + ---*a14*a16
4 2
a13=-------------------------------
2
a16
a12=0
a11=0
a10=0
a8=0
a7=2*a16
1 2
---*a14*a9 + a16
2
a6=-------------------
a16
2*a1*a16
a5=----------
a14
2*a1*a16
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:
b1,a16,a9,a14,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
1 2 2
df(u,t)=(u *a1*a14*a16 + ---*u *f(v,v)*a14 *a9 + u *f(v,v)*a14*a16
2x 2 x x
2 2 2
+ 2*u *a14 *a16*u + 2*f(v ,v )*a1*a16 + 2*f(v,v )*a1*a16
x x x 2x
2
+ f(v,v )*f(v,v)*a14*a16*a9 + 2*f(v,v )*a14*a16 *u)/(a14*a16)
x x
1 2 1 2 3
df(v,t)=( - ---*u *a14 *a9*v + ---*u *a14*a16 *v + v *f(v,v)*a16
4 x 2 x x
2 1 3 2
+ v *a14*a16 *u - ---*f(v,v )*a14*a16*a9*v + f(v,v )*a16 *v)/a16
x 2 x x
2 1 2
df(u,s)=(u *a1 *a14*a16*b1 + ---*u *f(v,v)*a1*a14 *a9*b1
3x 2 2x
2 2
+ 2*u *f(v,v)*a1*a14*a16 *b1 + 3*u *a1*a14 *a16*b1*u
2x 2x
2 2 2
+ 3*u *a1*a14 *a16*b1 + 10*u *f(v,v )*a1*a14*a16 *b1
x x x
2 2 2 3
+ u *f(v,v) *a14 *a16*a9*b1 + u *f(v,v) *a14*a16 *b1
x x
3 2 2
+ u *f(v,v)*a14 *a9*b1*u + 4*u *f(v,v)*a14 *a16 *b1*u
x x
3 2 2 2
+ 3*u *a14 *a16*b1*u + 6*f(v ,v )*a1 *a16 *b1
x x 2x
3
+ f(v ,v )*f(v,v)*a1*a14*a16*a9*b1 + 4*f(v ,v )*f(v,v)*a1*a16 *b1
x x x x
2 2 2
+ 6*f(v ,v )*a1*a14*a16 *b1*u + 2*f(v,v )*a1 *a16 *b1
x x 3x
3
+ f(v,v )*f(v,v)*a1*a14*a16*a9*b1 + 4*f(v,v )*f(v,v)*a1*a16 *b1
2x 2x
2 2 3
+ 6*f(v,v )*a1*a14*a16 *b1*u + 8*f(v,v ) *a1*a16 *b1
2x x
2 2 2
+ 2*f(v,v )*f(v,v) *a14*a16 *a9*b1 + 2*f(v,v )*f(v,v)*a14 *a16*a9*b1*u
x x
3 2 2 2 2
+ 4*f(v,v )*f(v,v)*a14*a16 *b1*u + 4*f(v,v )*a14 *a16 *b1*u )/(a1 *a14
x x
*a16)
1 2 1 2
df(v,s)=( - ---*u *a1*a14 *a9*b1*v + ---*u *a1*a14*a16 *b1*v
4 2x 2 2x
2 1 2
+ u *v *a1*a14*a16 *b1 - ---*u *f(v,v)*a14 *a16*a9*b1*v
x x 2 x
3 1 3
+ u *f(v,v)*a14*a16 *b1*v - ---*u *a14 *a9*b1*u*v
x 2 x
2 2 3 2 4
+ u *a14 *a16 *b1*u*v + 2*v *f(v,v )*a1*a16 *b1 + v *f(v,v) *a16 *b1
x x x x
3 2 2 2
+ 2*v *f(v,v)*a14*a16 *b1*u + v *a14 *a16 *b1*u
x x
1 3
- ---*f(v ,v )*a1*a14*a16*a9*b1*v + f(v ,v )*a1*a16 *b1*v
2 x x x x
1 3
- ---*f(v,v )*a1*a14*a16*a9*b1*v + f(v,v )*a1*a16 *b1*v
2 2x 2x
2 4
- f(v,v )*f(v,v)*a14*a16 *a9*b1*v + 2*f(v,v )*f(v,v)*a16 *b1*v
x x
2 3 2 2
- f(v,v )*a14 *a16*a9*b1*u*v + 2*f(v,v )*a14*a16 *b1*u*v)/(a1 *a16 )
x x