Solution 4 to problem l1o24
Expressions |
Parameters |
Relevance |
Back to problem l1o24
Expressions
The solution is given through the following expressions:
b39=0
b38=0
2
a4*a8 *b1
b37=-----------
3
a1
2
a4*a8 *b1
b36=-----------
3
a1
1 2
---*a4*a8 *b1
2
b35=---------------
3
a1
1
---*a4*a8*b1
2
b34=--------------
2
a1
1
---*a4*a8*b1
2
b33=--------------
2
a1
a4*a8*b1
b32=----------
2
a1
b31=0
b30=0
3
a8 *b1
b29=--------
3
a1
3 3
---*a8 *b1
2
b28=------------
3
a1
b27=0
2
3*a8 *b1
b26=----------
2
a1
3 2
---*a8 *b1
2
b25=------------
2
a1
3 2
---*a8 *b1
2
b24=------------
2
a1
b23=0
b22=0
a8*b1
b21=-------
a1
1
---*a8*b1
2
b20=-----------
a1
b19=0
b18=0
2
a4 *a8*b1
b17=-----------
3
a1
b16=0
2
3*a4*a8 *b1
b15=-------------
3
a1
2
3*a4*a8 *b1
b14=-------------
3
a1
3*a4*a8*b1
b13=------------
2
a1
3*a4*a8*b1
b12=------------
2
a1
6*a4*a8*b1
b11=------------
2
a1
3
---*a4*a8*b1
2
b10=--------------
2
a1
a4*b1
b9=-------
a1
3*a4*b1
b8=---------
a1
b7=0
3
4*a8 *b1
b6=----------
3
a1
2
12*a8 *b1
b5=-----------
2
a1
2
6*a8 *b1
b4=----------
2
a1
10*a8*b1
b3=----------
a1
4*a8*b1
b2=---------
a1
a10=0
a9=0
1
a7=---*a8
2
a6=0
a5=0
a3=0
a2=2*a8
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,a8,a4,a1
Relevance for the application:
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df(u,t)=u *a1 + 2*u *a8*u + f(v,v )*a4
2x x x
3 2 2
df(u,s)=(u *a1 *b1 + 4*u *a1 *a8*b1*u + 10*u *u *a1 *a8*b1
4x 3x 2x x
3 2 2 2 2
+ ---*u *f(v,v)*a1*a4*a8*b1 + 6*u *a1*a8 *b1*u + 12*u *a1*a8 *b1*u
2 2x 2x x
2 3 3
+ 6*u *f(v,v )*a1*a4*a8*b1 + 3*u *f(v,v)*a4*a8 *b1*u + 4*u *a8 *b1*u
x x x x
2
+ 3*f(v ,v )*a1 *a4*b1 + 3*f(v ,v )*a1*a4*a8*b1*u
x 2x x x
2
+ f(v,v )*a1 *a4*b1 + 3*f(v,v )*a1*a4*a8*b1*u
3x 2x
2 2 2 3
+ f(v,v )*f(v,v)*a4 *a8*b1 + 3*f(v,v )*a4*a8 *b1*u )/a1
x x
1
df(v,t)=---*u *a8*v + v *a8*u
2 x x
1 2 2 3 2
df(v,s)=(---*u *a1 *a8*b1*v + u *v *a1 *a8*b1 + ---*u *a1*a8 *b1*u*v
2 3x 2x x 2 2x
3 2 2 2
+ ---*u *a1*a8 *b1*v + 3*u *v *a1*a8 *b1*u
2 x x x
1 2 3 3 2
+ ---*u *f(v,v)*a4*a8 *b1*v + ---*u *a8 *b1*u *v
2 x 2 x
2 3 3
+ v *f(v,v )*a1*a4*a8*b1 + v *f(v,v)*a4*a8 *b1*u + v *a8 *b1*u
x x x x
1 1
+ ---*f(v ,v )*a1*a4*a8*b1*v + ---*f(v,v )*a1*a4*a8*b1*v
2 x x 2 2x
2 3
+ f(v,v )*a4*a8 *b1*u*v)/a1
x
df(u,t)=df(u,x,2)*a1 + 2*df(u,x)*a8*u + f(v,df(v,x))*a4$
df(u,s)=(df(u,x,4)*a1**3*b1 + 4*df(u,x,3)*a1**2*a8*b1*u + 10*df(u,x,2)*df(u,x)*
a1**2*a8*b1 + 3/2*df(u,x,2)*f(v,v)*a1*a4*a8*b1 + 6*df(u,x,2)*a1*a8**2*b1*u**2 +
12*df(u,x)**2*a1*a8**2*b1*u + 6*df(u,x)*f(v,df(v,x))*a1*a4*a8*b1 + 3*df(u,x)*f(v
,v)*a4*a8**2*b1*u + 4*df(u,x)*a8**3*b1*u**3 + 3*f(df(v,x),df(v,x,2))*a1**2*a4*b1
+ 3*f(df(v,x),df(v,x))*a1*a4*a8*b1*u + f(v,df(v,x,3))*a1**2*a4*b1 + 3*f(v,df(v,
x,2))*a1*a4*a8*b1*u + f(v,df(v,x))*f(v,v)*a4**2*a8*b1 + 3*f(v,df(v,x))*a4*a8**2*
b1*u**2)/a1**3$
df(v,t)=1/2*df(u,x)*a8*v + df(v,x)*a8*u$
df(v,s)=(1/2*df(u,x,3)*a1**2*a8*b1*v + df(u,x,2)*df(v,x)*a1**2*a8*b1 + 3/2*df(u,
x,2)*a1*a8**2*b1*u*v + 3/2*df(u,x)**2*a1*a8**2*b1*v + 3*df(u,x)*df(v,x)*a1*a8**2
*b1*u + 1/2*df(u,x)*f(v,v)*a4*a8**2*b1*v + 3/2*df(u,x)*a8**3*b1*u**2*v + df(v,x)
*f(v,df(v,x))*a1*a4*a8*b1 + df(v,x)*f(v,v)*a4*a8**2*b1*u + df(v,x)*a8**3*b1*u**3
+ 1/2*f(df(v,x),df(v,x))*a1*a4*a8*b1*v + 1/2*f(v,df(v,x,2))*a1*a4*a8*b1*v + f(v
,df(v,x))*a4*a8**2*b1*u*v)/a1**3$