A reformulation of an ordinary differential equation

TL;DR

This paper introduces a method to convert nonlinear ordinary differential equations into equivalent linear systems, potentially simplifying their solution or approximation processes.

Contribution

It presents a novel reformulation technique that transforms nonlinear ODEs into linear systems, facilitating easier analysis and computation.

Findings

Reformulation simplifies solving nonlinear ODEs.

Examples demonstrate the effectiveness of the method.

Potential for improved approximation techniques.

Abstract

The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able to open a new way in order to calculate or approximate the solution of an ordinary differential equation. Some examples are presented.