Hey!

I have pushed a branch which contains code to handle some forms of
separable partial equations.

I have currently only implemented basic support for multiplicative 
separate case, where u(x, t) = X(x)*T(t)

You can view/pull and comment the code on:
http://github.com/plaes/sympy/tree/pde-separate


A small example (or you can find some of them in the tests):

from sympy import *
from sympy import Derivative as D
u, X, T = map(Function, 'uXT')
x, t = symbols('xt')
c = symbols('c', Real=True)
# Define our function (one-dimensional wave equation)
eq = Eq(D(u(x, t), t, 2), D(u(x, t), x, 2)*c**2)
print pde_separate_mul(eq, u(x, t), [X(x), T(t)])

out >> D(T(t), t, t)/T(t) == c**2*D(X(x), x, x)/X(x)


PS. Has anyone examples of equations that can be separated using
additive separation: u(x, t) = X(x) + T(t)


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