Calculating the natural complete response of the system

Question

Problem:

A second order system satisfies the differential equation

                   d²x(t)/dt² + a₁ dx(t) + a_o x(t) = 0

1. Calculate the natural complete response Xn(t) of the system, provided that:
            a₀ = 13;           a₁ = 4;             x(0) = 1;                dx(o)/dt = 4.

A. X_n(t) = e ^-2t (cos3t - 2sin3t)

B. X_n(t) = e ^-3t (cos3t + 2sin3t)

C. X_n(t) = e ^-2t (cos3t + 2sin3t)

D. X_n(t) = e ^-2t (cos3t - 2sin3t)