A New Ring Theory Approach For Solving Cauchy-Euler differential Equations of Several Variables

TL;DR

This paper introduces a novel ring theory-based method for solving non-homogeneous Cauchy-Euler and Sturm-Liouville equations involving multiple variables, expanding the toolkit for differential equation solutions.

Contribution

It presents a new approach utilizing ponderation rings to find particular solutions of complex multi-variable differential equations, which is a novel application of ring theory.

Findings

Successfully applied the method to specific classes of equations.

Provides a systematic framework for solving multi-variable Cauchy-Euler equations.

Enhances existing solution techniques with ring theory concepts.

Abstract

In this article, we present an innovative method to find particular solutions of the non-homogeneous Cauchy-Euler equations in several variables and Sturm-Liouville equations. The method is basically built on the application of the ponderation ring which introduced by Assal and Zeyada [2].