Consider the differential equation: y''' + 4y'' + y = u(t)

y''(0) = 2, y'(0) = 1, y(0) = 0

where u(t) is the unit step function u(t) = { 1, t >=0 } and { 0, t < 0 }

a. Find the laplace transform Y(s) of y(t).

b. If the system with input u(t) has output z(t) = y'(t) where y(t) satisfies the above equation and all initial conditions are zero, find the relationship between the laplace transform of the input U(s) and the laplace transform of the output Z(s).