General Methods For Solving Ordinary Differential Equations 1

TL;DR

This paper introduces a new recursive method for solving arbitrary order linear ordinary differential equations with variable coefficients, simplifying the process under certain practical conditions.

Contribution

It presents a novel recursive and reduction-based approach for solving linear ODEs of any order with variable coefficients.

Findings

Arbitrary order linear ODEs with variable coefficients can be solved using the proposed method.

The method is applicable under conditions that are easily satisfied in practice.

It provides a systematic way to reduce complex differential equations to simpler forms.

Abstract

The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with variable coefficients can be solved by the method of recursion and reduction of order under some conditions which easily be satisfied in practical applications.