(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The solution to the ODE y''(t) + 4y(t) = 1 + u(t − 2), y(0) = 0, y'(0) = 0 is given by...

3. The attempt at a solution

OK well I figured this one is good to solve with Laplace transforms. So I took the Laplace of both sides to obtain (s^{2}+ 4)Y(s) = [e^{-2s}/s] + 1/s, which equals (e^{-2s}+ 1)/s. Isolating Y(s) gave me (e^{-2s}+ 1)/s(s^{2}+ 4). I used partial fraction expansion to obtain (1/4) - (1/4)cos2t, but this is apparently only half of the whole answer, given as (1/4)(1 − cos 2t) + (1/4)(1 − cos 2(t − 2))u(t − 2). What am I missing?

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# Homework Help: ODE with Laplace transform

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