Solving Linear Differential Equations by recursion and integrating factors

TL;DR

This paper introduces a recursive method combined with generalized integrating factors to solve first and second order linear differential equations, especially those with variable coefficients, providing explicit solutions when recursive patterns are identifiable.

Contribution

The paper presents a novel recursive solution technique with generalized integrating factors for linear differential equations, enhancing solution derivability for equations with variable coefficients.

Findings

Effective in solving differential equations with variable coefficients

Enables explicit solutions through identifiable recursive patterns

Applicable to classical physics-related differential equations

Abstract

In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in classical differential equations encountered in physics, inclusive of equations with variable coefficients, particularly when a pattern within the recursion is identifiable, thus enabling the derivation of an explicit expression for $y(x)$.