Consider & system described by the following third order differential equation; dy (t) dy (t) dy (t) + 6- +11 6y (t) = u (t) _ dt3 dt2 dt Compute the zero-state response of the system for the input u (t) = e 'p (t) . (Hint: 6s2 _ Is+6 = (s+1)(s+2)(s+3)) Compute the zero input response of the system for t 2 0, given that (0-) =1, y (07) = -1, i (07) = 1 Compute the output when the input is u (t) ~e-4'p (t) and the initial conditions are the same as those specified in part (b).