Re: [Axiom-developer] A question about differential equations

[Alasdair McAndrew]

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 <address@hidden> 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

--