Solving Ordinary Differential Equations with Variable Coefficients by Using the SEJI Transform

We have a new application that solves a set of ordinary differential equations with variable coefficients by using the suggested transform namely (Sadiq- Emad-Jinan) integral transform and denoted by “SEJ”I integral transform. In this paper a definition of the new transform is given and values of some elementary functions by using this transform, as well as the invers of this transform. Theorems are showed with proofs that used them in this work Also, some applications were introduced to explaining the method for solving ordinary differential equations with variable coefficients by using the suggested transform which can obtaining the exact solution.