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 = 1 + 8(t – 5), 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 piecewise-defined function and think about what happens to the graph of the solution at t = 5. y(t) = { = if 0 < t < 5, if 5 < t < c.

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