► Problem 1) Draw the system diagram and Find the output, given the input and initial conditions, for the systems described by the following differential or difference equations: Show your work step by step (a) x(t) = eu(t), y(0) 1 d 1 = = d² d d₁²y(t) + 5+ y(t) + 6y(t) = x(t) 4 d -- (b) x(t) = cos(t)u(t), y(0) = −- d² dt ¯¯ 5' dty (t)|1= = = d 3 5' dzy(t) + 3 y(t) + 2y(t) = 2x(t) dt (c) x[n] = u[n], y[-2] = 8, y[-1] = 0: - - - y[n] − ¼y[n − 2] = 2x[n] + x[n − 1] (d) x[n] = 2″u[n], y[−2] = 26, y[-1] = −1: - − − ( )x(n − 1] - y[n] − (4)y[n − 1] − (§)y[n − 2] = x[n] + -