First Integrals Without Integrating Factors or Symmetries

• A. J. Pan-Collantes ^[1]
  1. [1] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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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