Solution 8 to problem l112o13
Expressions |
Parameters |
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Back to problem l112o13
Expressions
The solution is given through the following expressions:
b42=0
b41=0
b40= - b39
b38=0
b37=0
b36=0
b35=0
b34= - b31
b33=0
b32=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
1
---*a5*b19
6
b23=------------
a0
1
---*a4*b19
6
b22=------------
a0
5 1
---*a0*a5*b19 + ---*a3*a4*b19
3 6
b21=-------------------------------
a0*a4
b20=0
1
b18=---*b19
2
4 1
---*a0*a5*b19 + ---*a3*a4*b19
3 3
b17=-------------------------------
2
a4
2 1
---*a0*a5*b19 + ---*a3*a4*b19
3 3
b16=-------------------------------
2
a4
2 1
---*a0*a5*b19 + ---*a3*a4*b19
3 3
b15=-------------------------------
2
a4
b14=0
b13=0
b12=0
1
---*a0*b19
3
b11=------------
a4
1
---*a0*b19
3
b10=------------
a4
a0*b19
b9=--------
a4
1
---*a0*b19
2
b8=------------
a4
1
---*a0*a3*b19
6
b7=---------------
2
a4
1
---*a0*a3*b19
2
b6=---------------
2
a4
b5=0
b4=0
b3=0
b2=0
1 2
---*a0 *b19
6
b1=-------------
2
a4
a8=0
a7=0
a2=0
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:
b39, b31, b19, a5, a3, a0, a4
Relevance for the application:
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2
df(u,t)=u *a0 + u *a6 + f(v,v )*a3 + f(v,v) *a5 + f(v,v)*a4*u
x x x
df(v,t)=v *a6
x
1 3 1 2 2
df(u,s)=(---*u *a0 *b19 + ---*u *f(v,v)*a0 *a4*b19 + u *f(v,v )*a0 *a4*b19
6 3x 2 2x x x
1 2 2 1 2
+ ---*u *f(v,v) *a0*a4 *b19 + ---*f(v ,v )*a0 *a3*b19
2 x 2 x 2x
2 2 1
+ ---*f(v ,v )*f(v,v)*a0 *a5*b19 + ---*f(v ,v )*f(v,v)*a0*a3*a4*b19
3 x x 3 x x
1 2 1 2
+ ---*f(v ,v )*a0 *a4*b19*u + ---*f(v,v )*a0 *a3*b19
3 x x 6 3x
2 2 1
+ ---*f(v,v )*f(v,v)*a0 *a5*b19 + ---*f(v,v )*f(v,v)*a0*a3*a4*b19
3 2x 3 2x
1 2 4 2 2
+ ---*f(v,v )*a0 *a4*b19*u + ---*f(v,v ) *a0 *a5*b19
3 2x 3 x
1 2 5 2
+ ---*f(v,v ) *a0*a3*a4*b19 + ---*f(v,v )*f(v,v) *a0*a4*a5*b19
3 x 3 x
1 2 2 2
+ ---*f(v,v )*f(v,v) *a3*a4 *b19 + f(v,v )*f(v,v)*a0*a4 *b19*u
6 x x
1 4 2 1 3 3 2
+ ---*f(v,v) *a4 *a5*b19 + ---*f(v,v) *a4 *b19*u)/(a0*a4 )
6 6
2
df(v,s)=v *f(v,v)*b31 + v *f(v,v) *b39 - f(v,v )*b31*v - f(v,v )*f(v,v)*b39*v
2x x 2x x