Solution 16 to problem l21o35
Expressions |
Parameters |
Relevance |
Back to problem l21o35
Expressions
The solution is given through the following expressions:
2
2*a11 *b1 + a7*a9*b1
b40=----------------------
2
a1
2 1
a11 *b1 + ---*a7*a9*b1
2
b39=------------------------
2
a1
6*a11*a9*b1
b38=-------------
2
a1
6*a11*a9*b1
b37=-------------
2
a1
3*a11*a9*b1
b36=-------------
2
a1
a11*b1
b35=--------
a1
3*a11*b1
b34=----------
a1
2*a11*b1
b33=----------
a1
2*a11*b1
b32=----------
a1
b31=0
b30=0
2
6*a9 *b1
b29=----------
2
a1
2
6*a9 *b1
b28=----------
2
a1
b27=0
b26=0
2*a9*b1
b25=---------
a1
a9*b1
b24=-------
a1
b23=0
3*a11*a7*b1
b22=-------------
2
a1
2
12*a11 *b1 + 6*a7*a9*b1
b21=-------------------------
2
a1
2 3
3*a11 *b1 + ---*a7*a9*b1
2
b20=--------------------------
2
a1
2
12*a11 *b1 + 6*a7*a9*b1
b19=-------------------------
a1*a9
2
3*a11 *b1 + a7*a9*b1
b18=----------------------
a1*a9
2
12*a11 *b1 + 6*a7*a9*b1
b17=-------------------------
a1*a9
2
9*a11 *b1 + 3*a7*a9*b1
b16=------------------------
a1*a9
24*a11*a9*b1
b15=--------------
2
a1
24*a11*a9*b1
b14=--------------
2
a1
10*a11*b1
b13=-----------
a1
30*a11*b1
b12=-----------
a1
20*a11*b1
b11=-----------
a1
20*a11*b1
b10=-----------
a1
18*a11*b1
b9=-----------
a1
4*a11*b1
b8=----------
a1
a11*b1
b7=--------
a9
5*a11*b1
b6=----------
a9
10*a11*b1
b5=-----------
a9
2
30*a9 *b1
b4=-----------
2
a1
20*a9*b1
b3=----------
a1
10*a9*b1
b2=----------
a1
a12=a11
a10=2*a9
a8=0
a6=4*a11
a5=2*a11
a1*a11
a4=--------
a9
3*a1*a11
a3=----------
a9
a2=6*a9
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,a11,a7,a9,a1
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(u,t)=(u *a1*a9 + 2*u *f(v,v)*a11*a9 + 6*u *a9 *u + 3*f(v ,v )*a1*a11
3x x x x 2x
+ f(v,v )*a1*a11 + f(v,v )*f(v,v)*a7*a9 + 4*f(v,v )*a11*a9*u)/a9
3x x x
df(v,t)=u *a9*v + v *f(v,v)*a11 + 2*v *a9*u + f(v,v )*a11*v
x x x x
2 2
df(u,s)=(u *a1 *a9*b1 + 4*u *f(v,v)*a1*a11*a9*b1 + 10*u *a1*a9 *b1*u
5x 3x 3x
2
+ 20*u *u *a1*a9 *b1 + 18*u *f(v,v )*a1*a11*a9*b1
2x x 2x x
+ 20*u *f(v ,v )*a1*a11*a9*b1 + 20*u *f(v,v )*a1*a11*a9*b1
x x x x 2x
2 2 3 2 2
+ 3*u *f(v,v) *a11 *a9*b1 + ---*u *f(v,v) *a7*a9 *b1
x 2 x
2 3 2
+ 24*u *f(v,v)*a11*a9 *b1*u + 30*u *a9 *b1*u
x x
2 2
+ 10*f(v ,v )*a1 *a11*b1 + 5*f(v ,v )*a1 *a11*b1
2x 3x x 4x
2
+ 9*f(v ,v )*f(v,v)*a1*a11 *b1 + 3*f(v ,v )*f(v,v)*a1*a7*a9*b1
x 2x x 2x
2
+ 30*f(v ,v )*a1*a11*a9*b1*u + 12*f(v ,v )*f(v,v )*a1*a11 *b1
x 2x x x x
2
+ 6*f(v ,v )*f(v,v )*a1*a7*a9*b1 + f(v,v )*a1 *a11*b1
x x x 5x
2
+ 3*f(v,v )*f(v,v)*a1*a11 *b1 + f(v,v )*f(v,v)*a1*a7*a9*b1
3x 3x
2
+ 10*f(v,v )*a1*a11*a9*b1*u + 12*f(v,v )*f(v,v )*a1*a11 *b1
3x 2x x
2
+ 6*f(v,v )*f(v,v )*a1*a7*a9*b1 + 3*f(v,v )*f(v,v) *a11*a7*a9*b1
2x x x
2 2
+ 12*f(v,v )*f(v,v)*a11 *a9*b1*u + 6*f(v,v )*f(v,v)*a7*a9 *b1*u
x x
2 2 2
+ 24*f(v,v )*a11*a9 *b1*u )/(a1 *a9)
x
df(v,s)=(u *a1*a9*b1*v + 2*u *v *a1*a9*b1 + 3*u *f(v,v)*a11*a9*b1*v
3x 2x x x
2
+ 6*u *a9 *b1*u*v + 2*v *f(v ,v )*a1*a11*b1 + 2*v *f(v,v )*a1*a11*b1
x x x x x 2x
2 2 1 2
+ v *f(v,v) *a11 *b1 + ---*v *f(v,v) *a7*a9*b1
x 2 x
2 2
+ 6*v *f(v,v)*a11*a9*b1*u + 6*v *a9 *b1*u + 3*f(v ,v )*a1*a11*b1*v
x x x 2x
2
+ f(v,v )*a1*a11*b1*v + 2*f(v,v )*f(v,v)*a11 *b1*v
3x x
2
+ f(v,v )*f(v,v)*a7*a9*b1*v + 6*f(v,v )*a11*a9*b1*u*v)/a1
x x