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Re: [Axiom-developer] A question about differential equations
From: |
Waldek Hebisch |
Subject: |
Re: [Axiom-developer] A question about differential equations |
Date: |
Sat, 17 Oct 2015 17:04:18 +0200 (CEST) |
> >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