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Consider the following initial value problem, in which an input of large amplitude and short duration...

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

y′′−4y′=δ(t−4), y(0)=6, y′(0)=0.

a. Find the Laplace transform of the solution.

b. Obtain the solution y(t).

c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t=4.

y(t)= ___ if 0 (less than or equal to) t <4, AND ___ if 4 (less than or equal to) t < infinity

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