Consider the initial value problem for function y given by,
$$y'' - 2y' + 17y = -2\delta(t-1),$$
$$y(0) = 0,$$
$$y'(0) = 0.$$
(a) Find the Laplace Transform of the source function, $F(s) = \mathcal{L}[-2\delta(t-1)]$.
$$F(s) = $$
(b) Find the Laplace Transform of the solution, $Y(s) = \mathcal{L}[y(t)]$.
$$Y(s) = $$
(c) Find the solution $y(t)$ of the initial value problem above.
$$y(t) = $$
Recall: If needed, the step function at c is denoted as $u(t-c)$.