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

I need to solve the following ODE using the laplace domain:

y' + 4y + 20(integral from 0->t)y(t)dt = 34e^-t on the interval 0<t<4 (y(0) = 0)

2. Relevant equations

I can solve the ODE fine, no problems. But I'm a little confused on how to evaluate it strictly on this interval. Would I need to utilize the step function somehow?

3. The attempt at a solution

This is what I did so far:

(sY(s) - 0) + 4Y(s) + 20Y(s) / s = 34 / (s + 1)

but this is not taking into account the interval...

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# Laplace transform on specific interval

Can you offer guidance or do you also need help?

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