Automatic Discontinuity Handling  

Solve a differential equation with discontinuities.

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X sol = NDSolve[{y'[t] == 15/4 - Floor[y[t]] + DiracDelta[t - 2], y[0] == .1}, y, {t, 0, 6}];

Plot the solution and its derivative.

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X Plot[Evaluate[{y[t], y'[t]} /. sol], {t, 0, 6}, PlotLegends -> {"y(t)", "y'(t)"}]

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