The rate equations are theoretical tools for research of the transient process of semiconductor lasers. Under the arbitrary intensity modulation, the rate equations were solved by using the small-signal approximation in order to analyze some properties of modulation response. The real and analytic solutions of the rate equations were obtained in these circumstances. And a specific example was given in which the modulation signal is a rectangular pulse current. Some properties of the modulation response were analyzed by the real and analytic solutions. The rigorous conditions of accuracy of the small-signal approximation were obtained. The approximate expressions of these conditions in some circumstances were obtained by the parameters of some semiconductor lasers.