Many of transient behaviours, which change their state from one steady-state to another steady-state involve more than one variable in the form of simultaneous differential equations and can only be solved numerically. It is therefore, concern of present paper to discuss solution of such equations by numerical intergration. A numerical example of the integration of differential equations describing the transient performance of an induction motor is investigated. A digital-computer program is described for the numerical evaluation of the transient using Runge-Kutta method of numerical integration. The total transient run-up time determined by steady-state approach involving graphical technique confirms the numerical solution of the differential equations.