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## Homework Statement

This is a problem from my book that I'm very close to finding the solution to, but I'm a little off. I have a feeling it's some small error I'm just overlooking because I'm so hungry/sleep-deprived. Anyway, the question asks you to find the Laplace transform of the given initial value problem. I've embedded my work.

## Homework Equations

The Laplace transform of first and second order derivatives and of cos(bt) and sin(bt) which are given in the book and I didn't type out because there are tables everywhere.

## The Attempt at a Solution

Thanks for any insight any of you might be able to give. Like I said, I feel like it's just something trivial, some negative sign, or some incorrect distribution of fractions that I'm overlooking.