Thank you!  In fact

normalize(sol.particular)

gives the same result.  But there's still an exp(-x) term in the particular
solution, which shouldn't be there, as exp(-x) is a basis solution.  So I
need some way of removing basis functions from the particular solution -
which possibly should be automatic.

On Sun, Oct 18, 2015 at 2:04 AM, Waldek Hebisch <[email protected]>
wrote:

> > >In putting Axiom through its paces just recently (yes: Axiom, not a
> fork!),
> > >I experimented with the ODE
> > >
> > >y''+6y'+5y = 10x^2+4x+4exp(-x)
> > >
> > >Now standard techniques (such as I teach my students), produce a
> solution
> > >of the form
> > >
> > >y = A*exp(-5x)+B*exp(-x)+2*x^2-4*x+4+x*exp(-x).
> > >
> > >This is Axiom:
> > >
> > >--(View this section in a fixed width font if it isn't shown as such)
> > >
> > >(1) -> y:=operator 'y
> > >(2) -> deq:=D(y(x),x,2)+6*D(y(x),x)+5*y(x)=10*x^2+4*x+4*exp(-x)
> > >(3) -> sol:=solve(deq,y,x)
> > >   (3)
> > >   [
> > >       particular =
> > >             - x 6       2               - x 5     - 5x  - x     2  - 5x
> > >       4x (%e   )  + (10x  - 16x + 16)(%e   )  - %e    %e    - 2x %e
> > >       -----------------------------------------------------------------
> > >                                       - x 5
> > >                                   4(%e   )
> > >     ,
> > >              - x   - 5x
> > >    basis= [%e   ,%e    ]]
> > >Type: Union(Record(particular: Expression(Integer),basis:
> > >List(Expression(Integer)))
> > >
> > >--
> > >of which the particular solution is a bit of a jumble.   It doesn't
> seem to
> > >be particularly simplifiable
>
> try
>
> eval(sol.particular, exp(-5*x)= exp(-x)^5)
>
> --
>                               Waldek Hebisch
>



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