Consider the following initial value problem:
$x'' - 4x' - 32x = \sin(3t)$, $x(0) = 2$, $x'(0) = -1$.
Using $X$ for the Laplace transform of $x(t)$, i.e., $X = \mathcal{L}\{x(t)\}$, find the equation you get by taking the Laplace transform of the differential
equation and solve for
$X(s) = $ help (formulas)