Solution 3 to problem l1o24
Expressions |
Parameters |
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Back to problem l1o24
Expressions
The solution is given through the following expressions:
b39=0
3
16*a10 *b1
b38=------------
2
a1*a4
2
- 16*a10 *b1
b37=---------------
a1*a4
b36=0
2
- 4*a10 *b1
b35=--------------
a1*a4
2*a10*b1
b34=----------
a1
2*a10*b1
b33=----------
a1
b32=0
b31=0
4
- 128*a10 *b1
b30=----------------
4
a4
b29=0
3
192*a10 *b1
b28=-------------
3
a4
b27=0
b26=0
2
- 24*a10 *b1
b25=---------------
2
a4
2
- 32*a10 *b1
b24=---------------
2
a4
b23=0
b22=0
b21=0
2*a10*b1
b20=----------
a4
b19=0
b18=0
b17=0
b16=0
2
16*a10 *b1
b15=------------
a1*a4
2
16*a10 *b1
b14=------------
a1*a4
- 8*a10*b1
b13=-------------
a1
- 8*a10*b1
b12=-------------
a1
- 12*a10*b1
b11=--------------
a1
- 2*a10*b1
b10=-------------
a1
a4*b1
b9=-------
a1
3*a4*b1
b8=---------
a1
b7=0
3
- 256*a10 *b1
b6=----------------
3
a4
2
192*a10 *b1
b5=-------------
2
a4
2
96*a10 *b1
b4=------------
2
a4
- 40*a10*b1
b3=--------------
a4
- 16*a10*b1
b2=--------------
a4
2
- 8*a10 *a1
a9=--------------
2
a4
a8=0
2*a10*a1
a7=----------
a4
a6=0
a5=0
a3=0
- 8*a10*a1
a2=-------------
a4
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,a10,a4,a1
Relevance for the application:
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2
u *a1*a4 - 8*u *a10*a1*u + f(v,v )*a4
2x x x
df(u,t)=-----------------------------------------
a4
3 2 2
df(u,s)=(u *a1*a4 *b1 - 16*u *a10*a1*a4 *b1*u - 40*u *u *a10*a1*a4 *b1
4x 3x 2x x
3 2 2
- 2*u *f(v,v)*a10*a4 *b1 + 96*u *a10 *a1*a4*b1*u
2x 2x
2 2 3
+ 192*u *a10 *a1*a4*b1*u - 12*u *f(v,v )*a10*a4 *b1
x x x
2 2 3 3
+ 16*u *f(v,v)*a10 *a4 *b1*u - 256*u *a10 *a1*b1*u
x x
4 3 4
+ 3*f(v ,v )*a4 *b1 - 8*f(v ,v )*a10*a4 *b1*u + f(v,v )*a4 *b1
x 2x x x 3x
3 2 2 2 3
- 8*f(v,v )*a10*a4 *b1*u + 16*f(v,v )*a10 *a4 *b1*u )/(a1*a4 )
2x x
2 2 2
2*u *a10*a1*a4*v + f(v,v)*a10*a4 *v - 8*a10 *a1*u *v
x
df(v,t)=------------------------------------------------------
2
a4
3 2 2
df(v,s)=(2*u *a10*a1*a4 *b1*v - 32*u *a10 *a1*a4 *b1*u*v
3x 2x
2 2 2 2 3
- 24*u *a10 *a1*a4 *b1*v - 4*u *f(v,v)*a10 *a4 *b1*v
x x
3 2 4
+ 192*u *a10 *a1*a4*b1*u *v + 2*f(v ,v )*a10*a4 *b1*v
x x x
4 2 3
+ 2*f(v,v )*a10*a4 *b1*v - 16*f(v,v )*a10 *a4 *b1*u*v
2x x
3 2 2 4 4 4
+ 16*f(v,v)*a10 *a4 *b1*u *v - 128*a10 *a1*b1*u *v)/(a1*a4 )
df(u,t)=(df(u,x,2)*a1*a4 - 8*df(u,x)*a10*a1*u + f(v,df(v,x))*a4**2)/a4$
df(u,s)=(df(u,x,4)*a1*a4**3*b1 - 16*df(u,x,3)*a10*a1*a4**2*b1*u - 40*df(u,x,2)*
df(u,x)*a10*a1*a4**2*b1 - 2*df(u,x,2)*f(v,v)*a10*a4**3*b1 + 96*df(u,x,2)*a10**2*
a1*a4*b1*u**2 + 192*df(u,x)**2*a10**2*a1*a4*b1*u - 12*df(u,x)*f(v,df(v,x))*a10*
a4**3*b1 + 16*df(u,x)*f(v,v)*a10**2*a4**2*b1*u - 256*df(u,x)*a10**3*a1*b1*u**3 +
3*f(df(v,x),df(v,x,2))*a4**4*b1 - 8*f(df(v,x),df(v,x))*a10*a4**3*b1*u + f(v,df(
v,x,3))*a4**4*b1 - 8*f(v,df(v,x,2))*a10*a4**3*b1*u + 16*f(v,df(v,x))*a10**2*a4**
2*b1*u**2)/(a1*a4**3)$
df(v,t)=(2*df(u,x)*a10*a1*a4*v + f(v,v)*a10*a4**2*v - 8*a10**2*a1*u**2*v)/a4**2$
df(v,s)=(2*df(u,x,3)*a10*a1*a4**3*b1*v - 32*df(u,x,2)*a10**2*a1*a4**2*b1*u*v -
24*df(u,x)**2*a10**2*a1*a4**2*b1*v - 4*df(u,x)*f(v,v)*a10**2*a4**3*b1*v + 192*df
(u,x)*a10**3*a1*a4*b1*u**2*v + 2*f(df(v,x),df(v,x))*a10*a4**4*b1*v + 2*f(v,df(v,
x,2))*a10*a4**4*b1*v - 16*f(v,df(v,x))*a10**2*a4**3*b1*u*v + 16*f(v,v)*a10**3*a4
**2*b1*u**2*v - 128*a10**4*a1*b1*u**4*v)/(a1*a4**4)$