First Integrals Without Integrating Factors or Symmetries

descriptionPublicationkeyboard_double_arrow_right Article 24 Jan 2025Publisher:Qeios LtdJournal:Qualitative Theory of Dynamical Systems, volume 24 (issn: 1575-5460, eissn: 1662-3592,

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Authors: A. J. Pan-Collantes;

doi: 10.32388/aniiui.2 , 10.32388/aniiui , 10.1007/s12346-025-01378-9

First Integrals Without Integrating Factors or Symmetries

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Abstract

A new method for finding first integrals of ordinary differential equations (ODEs) is presented. The approach is based on the complete integrability of the Pfaffian system associated with the ODE, defined on a suitable jet space. Remarkably, the method does not require the use of symmetries or integrating factors. Examples of second-, third-, and fourth-order ODEs are provided to illustrate the method, including cases where classical approaches fail. This work extends the range of tools available for the analysis and solution of ODEs.

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University of Cádiz
Spain

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