Consider the following functions Y_i(s) = L[y_i(t)], i = 1, 2 and 3,

where {y_i(t), i = 1, 2, 3} are the complete responses of differential equations with zero initial conditions.

(a) For each of these functions determine the corresponding differential equation, if all of them have as input x(t) = u(t).

(b) Find the general form of the complete response {y_i(t), i = 1, 2, 3} for each of the {Y_i(s) i = 1, 2, 3}. Use MATLAB to plot the poles and zeros for each of the {Y_i(s)}, to find their partial fraction expansions and the complete responses.

s+1 Y,(s) = s(s ,Y,(s) : s(s + 1) +9) (s + 2) 2.Y3(s) + 2s + 4) %3D