Laplace transforms are on your ideas list.  Pardon me if I am slightly
ignorant, as we have just started learning about these, but part the
thing that makes Laplace transforms so great for solving ODEs is that
taking the Laplacian of a differential gives you back the initial
conditions of the function (assuming the solution doesn't grow faster
than e^x).  So far, dsolve doesn't even include a way to include
initial conditions (another thing to implement).  But yes, taking the
Laplacian of a regular function should be as simple as plugging it
into the definition, assuming sympy's integration engine can support
it (which it usually should, as most are just integration by parts
with simple improper limits).

But never mind that.  I think that I could fill a whole summer just
implementing what I have already learned, especially considering
things like variation of parameters and substitutions.

I tried implementing that patch, but so far I am having a couple of
stumbling blocks.  Pardon me again if I sound ignorant, but  as I have
said, I have never worked with an open source project before.  I have
also had very little experience with modules (basically, I was taught
them, but I have never tried to make any, and so I have forgotten how
they work).

My problem is this:  how do I edit the source so I can test it.  So
far, the only way I can see to do this is to reinstall with setup.py
each time I make an edit, then reload python.  Aside from having many
steps, this forces me to overwrite my released version of sympy with
the version that I am working on, which I don't necessarily want to
do.  Is there a way I can test this from a separate directory.  By the
way, I am running Mac OS X 10.5.

Also, as I predicted, I am having difficulties understanding the match
function that the ODE solving functions use.  How exactly does this
work?  As far as I can tell, it returns a dictionary of the variables
of the function, but what are these set to.  I probably could figure
this one out, but as I said above, I currently don't know how to test
this very efficiently.

And of course, if I actually manage to churn out something that works,
I have no idea how to submit it.

Sorry about all that.

Aaron
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