Non-limit integration of differential equations. General solution for van der Pol equation

TL;DR

This paper introduces a new method for integrating differential equations based on physical principles, successfully deriving general solutions for the van der Pol equation, heat equation, and free oscillator.

Contribution

It presents a novel integration method for ODEs and PDEs, providing the first general solution for the van der Pol equation using this approach.

Findings

General solution for van der Pol equation obtained

Method applicable to heat equation and free oscillator

New physical-based integration technique proposed

Abstract

Using the physical background based on the earlier author's researches the new method of the ODE and PDE integration is proposed. As illustrations of the method the general solution for free oscillator and for heat equation are derived. As a result of the article the general solution for van der Pol equation is given.