Comment #27 on issue 2128 by someb...@bluewin.ch: Implement more general
piecewise integration algorithm
http://code.google.com/p/sympy/issues/detail?id=2128
There is another reference which might give quite some insight:
"Symbolic Solutions of Discontinuous Differential Equations"
by Martin von Mohrenschildt. Its his thesis from 1994.
Part of the abstract looks very promising:
"Our idea is to extend differential fields with discontinuous functions.
This extension should be natural, such that the basic results, such
as the Risch structure theorem and the algorithm solving the Risch
differential
equation, can be extended to handle these discontinuous extensions.
We generalize the basic notations and theorems of the Liouville-Ritt-Risch
theory to a theory of closed-form solutions of discontinuous field
extensions.
"
An implementation would be a major undertaking probably.
OTOH they have done (at least a partial) one for Maple in 1994.
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