1) A LTIC system is specified by the equation

(D² + 5D + 6)y(t) = (D+1)x(t)

1

a) Find the characteristic polynomial, characteristic equation, characteristic roots, and

characteristic modes of this system.

b) Find the zero-input response yzi(t) if the initial conditions of the system are yzi (0) =

2 and ₂i(0-) = -1.