Journal of Informatics and Mathematical Sciences Vol. 7, No. 2, pp. 93–97, 2015 ISSN 0975-5748 (online); 0974-875X (print) Published by RGN Publications http://www.rgnpublications.com Application of Laplace Transforms to Solve ODE using M ATLAB Research Article Purnima Rai Department of Mathematics, Sadabai Raisoni Women’s College, Nagpur, Maharashtra, India purnima.rai411@gmail.com Abstract. Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. With the increasing complexity of engineering problems, Laplace transforms help in solving complex problems with a very simple approach just like the applications of transfer functions to solve ordinary differential equations. In this paper we present a new technological approach to solve Ordinary differential equation. The application of MATLAB to compute and visualize the Laplace transforms is also discussed. Keywords. Laplace transforms; Ordinary differential equation (ODE); MATLAB MSC. 44A10; 68N01 Received: May 11, 2015 Accepted: June 28, 2015 Copyright © 2015 Purnima Rai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Laplace transforms [1] are frequently used in solving physical problems which involve integral and ordinary differential equations with constant coefficients as those arising in the analysis of electronic circuits. As a consequence of this most of them not only may be quickly computed with the aid of computer algebraic systems but the most commonly used mathematical software have also got subroutines that facilitate its handling and even force the general solving methods to use them. One of such powerful software packages is MATLAB [2], [3], [5], [6], [7] that contains many easy to use tools and built-in functions to solve or simulate differential equations by Laplace transform.