Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y' + 1672y = 4r8(t 2) ,
y(0) = 0, y (0) = 0.
a. Find the Laplace transform of the solution
Y(s) = L {ylt)}
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 = 2.
if 0 < t < 2,
if 2 < t < 0.