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

  1. Find the Laplace transform of the solution.

    [math]

  2. Obtain the solution [math].

    [math]

  3. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at [math].

    [math] [math]  [math]

    [math]