Solution 28 to problem l112o23
Expressions |
Parameters |
Relevance |
Back to problem l112o23
Expressions
The solution is given through the following expressions:
b41=0
b40=0
1 2 2
---*a14 *a4 *b1
4
b39=-----------------
4
a1
b38=0
b37=0
2
a14 *a4*b1
b36=------------
3
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
- a4*b42
b23=-----------
a1
b22=0
1 2 3
---*a14 *a4 *b1
2
b21=-----------------
5
a1
b20=0
2 2
2*a14 *a4 *b1
b19=---------------
4
a1
3 2 2
---*a14 *a4 *b1
4
b18=-----------------
4
a1
2
2*a14*a4 *b1
b17=--------------
3
a1
3 2
---*a14*a4 *b1
2
b16=----------------
3
a1
3 2
---*a14*a4 *b1
2
b15=----------------
3
a1
b14=0
2
2*a14 *a4*b1
b13=--------------
3
a1
2
3*a14 *a4*b1
b12=--------------
3
a1
3*a14*a4*b1
b11=-------------
2
a1
3*a14*a4*b1
b10=-------------
2
a1
5*a14*a4*b1
b9=-------------
2
a1
3
---*a14*a4*b1
2
b8=---------------
2
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
1
---*a14*a4
2
a16=------------
a1
a15=0
a13=0
a12=0
a11=0
a10=0
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:
b42,b1,a4,a14,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
2
a1
1
---*v *f(v,v)*a14*a4 + v *a1*a14*u
2 x x
df(v,t)=------------------------------------
a1
5 3 3 4
df(u,s)=(u *a1 *b1 + ---*u *f(v,v)*a1 *a14*a4*b1 + 3*u *a1 *a14*b1*u
3x 2 2x 2x
2 4 3
+ 3*u *a1 *a14*b1 + 5*u *f(v,v )*a1 *a14*a4*b1
x x x
3 2 2 2 2 2
+ ---*u *f(v,v) *a1*a14 *a4 *b1 + 3*u *f(v,v)*a1 *a14 *a4*b1*u
4 x x
3 2 2 4
+ 3*u *a1 *a14 *b1*u + 3*f(v ,v )*a1 *a4*b1
x x 2x
3 2 2 3
+ ---*f(v ,v )*f(v,v)*a1 *a14*a4 *b1 + 3*f(v ,v )*a1 *a14*a4*b1*u
2 x x x x
4 3 2 2
+ f(v,v )*a1 *a4*b1 + ---*f(v,v )*f(v,v)*a1 *a14*a4 *b1
3x 2 2x
3 2 2 2
+ 3*f(v,v )*a1 *a14*a4*b1*u + 2*f(v,v ) *a1 *a14*a4 *b1
2x x
1 2 2 3 2 2
+ ---*f(v,v )*f(v,v) *a14 *a4 *b1 + 2*f(v,v )*f(v,v)*a1*a14 *a4 *b1*u
2 x x
2 2 2 4 4 5
+ 2*f(v,v )*a1 *a14 *a4*b1*u - f(v,v) *a1 *a4*b42)/a1
x
3 2
df(v,s)=(u *v *a1 *a14*b1 + v *f(v,v )*a1 *a14*a4*b1
x x x x
1 2 2 2 2
+ ---*v *f(v,v) *a14 *a4 *b1 + v *f(v,v)*a1*a14 *a4*b1*u
4 x x
2 2 2 3 4 4
+ v *a1 *a14 *b1*u + f(v,v) *a1 *b42*v)/a1
x