Using Anuj Transform to Solve Ordinary Differential Equations with Variable Coefficients

Abstract

In this paper, a new integral transform was applied to find the solution of ordinary differential equations with variable coefficients because of its importance in various fields of science, especially mathematics. This integral transform is called Anuj transform. The Anuj transform is one of the modern integral transforms that is effective in solving ordinary differential equations in general and ordinary differential equations with variable coefficients in particular. In order to achieve this; and based on a set of relations that have been included in this paper, we have implemented a number of methods to reach important formulas and results. These results have been applied to different set of problems of ordinary differential equations with variable coefficients. The solutions of those problems were reached in a smooth manner, based on some basics of ordinary differential equations which give a simple and clear idea of using the Anuj transform to solve ordinary differential equations with variable coefficients.