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

y? + y = 8 + ? (t-2), y(0) = 0.

a. Find the Laplace transform of the solution.

Y(s) = L {y(t)} =

b. Obtain the solution y(t).

y(t) =

c. Express the solution as a piece wise-defined function and think about what happens to the graph of the solution at t = 2.

y(t) = if 0 < t < 2, if 2 < t