Problems:

1. [20 points] Determine whether the below systems are linear or non-linear.
2. dy/dt + 2y(t) = f²(t)
3. dy/dt + 3ty(t) = t²f(t)

2. [40 points]

1. 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).

1. 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]

1. Find the unit impulse response h[k] of the following system: y[k+1] + 2y[k] = f[k].
2. 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].