Simplification



I have a function which looks like

            - 9 t
  f (t) = %e

       6 (9 c  + 43 c  + 10 c )   2 (6 c  - 58 c  + 50 c )
             3       2       1          3       2       1
    (- ------------------------ - ------------------------) sin(3 t)
                  5                          5
   (----------------------------------------------------------------
                                   6
                                                                 - 15 t
     (9 c  + 43 c  + 10 c ) cos(3 t)    (9 c  + 28 c  + 10 c ) %e
         3       2       1                  3       2       1
   + -------------------------------) - -------------------------------
                   15                                 15

It's an example solution obtained by desolve(...) for system of linear ODEs 
with constant coefficients:

  (%o1) desolve(['diff(f[1](t),t,1)-3*f[3](t)-15*f[2](t)+12*f[1](t) = 0,
                 'diff(f[2](t),t,1)+3*f[3](t)+12*f[2](t)+12*f[1](t) = 0,
                 'diff(f[3](t),t,1)+9*f[3](t)+26*f[2](t)-34*f[1](t) = 0],
                [f[1](t),f[2](t),f[3](t)])$
  (%o2) at(%,makelist(f[i](0)=c[i],i,1,3));

How it could be simplified to

  f(t) = exp(a_1 t) (sin(b_1 t) P_1 + cos(b_1 t) Q_1) +
         exp(a_2 t) (sin(b_2 t) P_2 + cos(b_2 t) Q_2) + ...

Where P_i and Q_i are polynomials over c_i and t (with expanded coefficients)?

I'm not so strong in Maxima simplification and patterns so I don't know a 
straightforward way to do it.

-- 
Alexey Beshenov <al at beshenov.ru>
http://beshenov.ru/
-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: application/pgp-signature
Size: 189 bytes
Desc: not available
Url : http://www.math.utexas.edu/pipermail/maxima/attachments/20080325/36e69051/attachment.pgp