# Laplace transform and initial value problems

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1. Find the Laplace transforms of

2. Use the Laplace transforms to solve the initial value problem

y'' + 2y' - 8y = 0, y(0) = 1, y'(0) = 8

3. Solve the initial value problem y'' + 2y = r(t), y(0) = y'(0) = 0

Where r(t) = 1 for 0 <t <1 and r(t) =0 otherwise

4. Solve the initial value problem

y" + 2y' + y = delta(t) + U(t), y(0) = 0, y'(0) = 1

5. Find the inverse Laplace transform of F(s) using the convolution theorem.

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#### Solution Summary

The solution is comprised of step-by-step explanations of using inverse Laplace transforms to solve differential equations. Furthermore, it shows how to apply convolution theorem to find the inverse Laplace transform.

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