## Description

1. [20 points] Determine whether the below systems are linear or non-linear.

a. dy/dt + 2y(t) = f2

(t)

b. dy/dt + 3ty(t) = t2

f(t)

2. [40 points]

a. For the LTIC system with the below system equation, find the zeroinput response (y0(t)) where the initial conditions are y0(0) = 2 and

dy0(0) / dt = -1.

(D2+5D+6) y(t) = (D+1) f(t).

b. For the LTIC system with the unit impulse response of h(t) = e-t u(t).

Find the zero state response of the system y(t) if input is f(t) = u(t).

3. [40 points]

a. Find the unit impulse response h[k] of the following system: y[k+1] +

2y[k] = f[k].

b. Determine the zero-state response of the LTID system with the unit

impulse response of h[k] = (-2)k u[k] if the input f[k] = e

-k u[k].