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This is a Quantitative Study study.

September 18, 2025Open Access

First Integrals Without Integrating Factors or Symmetries

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The method identifies first integrals without the need for integrating factors or symmetries, enhancing problem-solving.
Significant examples include second-, third-, and fourth-order ODEs, demonstrating the method's broad applicability.
The approach utilizes the complete integrability of the Pfaffian system on a suitable jet space to analyze ODEs.
This work potentially broadens the toolkit for tackling challenging ordinary differential equations.

Implication

This method identifies first integrals in ODEs without symmetries or integrating factors, expanding analytical capabilities.

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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Cite This Study

Antonio J. Pan-Collantes (2025) studied this question.

synapsesocial.com/papers/68d462d231b076d99fa62434 https://doi.org/10.32388/aniiui.2

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Implication

This method identifies first integrals in ODEs without symmetries or integrating factors, expanding analytical capabilities.

First Integrals Without Integrating Factors or Symmetries

Key Points

Implication

Abstract

Discussion

Cite This Study

First Integrals Without Integrating Factors or Symmetries

Key Points

Implication

Abstract

Discussion

Cite This Study

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