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Laplace transforms, Inverse Laplace transforms, & Diff Eqns

Please walk me through these problems step by step.

1. Compute the Laplace transform of e^(-10t) = u(t).

2. Compute the inverse Laplace transform of:

X(s) = (3s^2+2s+1) / (s^3+5s^2+8s+4)

3. Use Laplace transforms to compute the solution to the differential equation given in the attachment.