Comment #14 on issue 1621 by krastano...@gmail.com: Initial conditions in dsolve()
http://code.google.com/p/sympy/issues/detail?id=1621

This and more is already implemented in the pull request mentioned above.

The issues with it are *not* related to math, but to integration in the current code base.

On another note, I personally dislike the API you are proposing, because it has very restricted domain of applicability (but there is no consensus on this, so feel free to investigate more).

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