Use the Laplace transform to solve the following initial value problem:

First, using $Y$ for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L} \lbrace y(t) \rbrace$,
find the equation you get by taking the Laplace transform of the differential equation
$=0$

Now solve for $Y(s) =$

By completing the square in the denominator and inverting the transform, find
$y(t)=$ .

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