Blackboard Problem 2, ECE 330 Signals and Systems, Lec. 1

Use Laplace Transforms to solve the following two differential equations with initial conditions:

1)   y''(t) + 5 y'(t) +  6 y(t) = exp(-t)u(t),  y(0) = 1, y'(0) = -1.

Solution: y(t) = [ .5 e^{-t} + e^{-2t} - .5 e^{-3t} ] u(t)

2)   y''(t) + 9 y'(t) + 20 y(t) = cos(t)u(t),   y(0) = 0, y'(0) =  0.