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 > -- [image: http://www.facebook.com/alasdair.mcandrew] <http://www.facebook.com/alasdair.mcandrew> [image: https://plus.google.com/+AlasdairMcAndrew/posts] <https://plus.google.com/+AlasdairMcAndrew/posts> [image: https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108] <https://www.linkedin.com/pub/alasdair-mcandrew/a/178/108> [image: https://twitter.com/amca01] <https://twitter.com/amca01> [image: http://numbersandshapes.net] <http://numbersandshapes.net>
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