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Surf these sites:
 Introduction to Ordinary Differential Equations with Mathematica -- Contains a number of ODE labs, and an extremely useful Mathematica Package ode.m which allows series solutions of ODEs.
Partial Differential Equations -- A set of lectures on numerical solutions and applications to physics.
Series Solutions to Differential Equations -- A set of downloadable lectures.
Vibrating Drumhead -- A set of Mathematica packages which outline solutions of the wave equation in various coordinates.

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