A new method of obtaining the impulse response of second-order time varying systems of the form a2(t)x″ + a1(t)x′ + ao(t)x = f(t) without the knowledge of the independent solutions of the associated homogeneous equation is presented. The proposed procedure amounts to obtaining the particular solution of the equation: (N′ + N2)a2 + 2a2′N + a2″ = a1′ + a1N − a0, prime denotes differentiation. Many examples are given to indicate the unique feature of the method.