Problem 7. Using Laplace transforms, find the solution $y(t)$ to the linear ordinary differential equation
$\ddot{y}(t) + 7\dot{y}(t) + 12y(t) = \dot{u}(t) - u(t)$,
where $u(t) = e^{-t}$, $\dot{y}(0) = 0$, and $y(0) = 0$. Note that this is the forced response because the initial conditions are zero.
