The purpose of this research is to perform a comparative numerical analysis of an efficient numerical methods for second-order ordinary differential equations, by reducing the second-order ODE to a system of first-order differential equations. Then we obtain approximate solutions to the system of ODE. To validate the accuracy of the algorithm, a comparison between Euler's method and the Runge-Kutta method or order four was carried out and an exact solution was found to verify the efficiency, accuracy of the methods. Graphical representations of the parametric plots were also presented. Time inference analysis is taken to check the time taken to executes the algorithm in Mathematica®12.2.0. The obtained approximate solution using the algorithm shows that the Runge-Kutta method of order four is more efficient for solving system of linear ordinary differential equations.