Solve the following given y(0) = 0 & y'(0)=1:(adsbygoogle = window.adsbygoogle || []).push({});

y′′+3y′+2y = u_{2}(t), such that u_{2}(t) is a heaviside step function

Here's what I've got so far,

=>s^{2}Y(s)−sy(0)−y′(0) + 3sY(s)−3y(0) + 2Y(s)= exp(−2s)/s

Y(s) = (exp(−2s) + s) / (s(s^{2}+3s+2))

Y(s) = exp(−2s)/(s(s^{2}+3s+2))* + 1/(s^{2}+3s+2)**

The second part, **, I was able to solve with partial fractions => 1/(s+1) − 1/(s+2) which transforms to exp(−t) − exp(−2t).

However I don't know how to solve the first part, *, since the step function isn't by itself,

Any push in the right direction would be great,

Thanks in advance

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# Homework Help: Initial Value Problem with Laplace Transforms

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