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Interpret a case discrimination in a differential equation solution?

Posted 5 months ago
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Hey Guys,

I have a question. I'm trying to solve a differential equation. I have a solution, but I can't work with it. Mathematica makes a case distinction, but I do not know how to interpret this? Anybody have an idea? What does the Mod mean? Thank you for your help.

My code

The solution that you found is wrong, as it is discontinuous. We get a continuous solution if we give a bounded interval as domain forĀ t:

sol = With[{a = 1, b = 1, x0 = 1, v0 = 0}, 
   DSolveValue[{a*x''[t] + b*x'[t] == SquareWave[t], x[0] == x0, 
     x'[0] == v0},
    x, {t, 0, 5}]];
PiecewiseExpand[sol[t]]
Plot[sol[t], {t, 0, 5}]
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