[Axiom-mail] A question about differential equations

[Alasdair McAndrew]

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