Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.

1. Find the Laplace transform of the solution.

$\displaystyle Y(s) = {\mathcal L}\left\lbrace y(t) \right\rbrace =$

2. Obtain the solution $y(t)$.

$y(t) =$

3. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at $t = 3$.

 $y(t) =$ $\displaystyle \Bigg\lbrace$ $\ \mbox{ if } \ 0 \leq t < 3,$ $\ \mbox{ if } \ 3 \leq t < \infty.$