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