3) A LTIC system is specified by the equation (D2+5D+6)y(t) = (D+1)x(t) a) Find the characteristic polynomial, characteristic equation, characteristic roots, and characteristic modes corresponding to each characteristic root. b) Find the zero-input response yzi(t) for t≥ 0 if the initial conditions are yzi (0) = 2 and zi (0) = = -1. 4) A LTIC system is specified by the equation (D+ 1)(D²+5D+6)y(t) = Dx(t) d² dt2 with yzi(0)=2, Yzi (0) = =-1, and 2Yzi (0¯) = 5, ⚫ find the zero-input response Yzi(t). ⚫ find the impulse response h(t) (i.e., the zero-state response for input x(t) = 8(t) with zero initial conditions).