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:
(4) -> simplifyExp(sol.particular)
(4) ->
2 - 5x - 6x
(8x - 16x + 16)%e + (4x - 1)%e
(4) ---------------------------------------
- 5x
4%e
--
Is there some way I can coerce Axiom into giving a particular solution to
such a straightforward ODE in a more simplified form?
Many thanks,
Alasdair
[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>
_______________________________________________
Axiom-mail mailing list
[email protected]
https://lists.nongnu.org/mailman/listinfo/axiom-mail
