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arXiv · 2404.14352

Integration of first-order ODEs by Jacobi fields

A. J. Pan-Collantes·J. A. Alvarez-Garcia
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Abstract

A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between 2-dimensional Riemannian manifolds and the integrability of first-order ODEs, which was established in a previous work of the authors. An integration procedure is provided, together with several examples to illustrate it. A connection between integrating factors of first-order ODEs and Schr\"odinger-type equations is highlighted.

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A. J. Pan-Collantes, J. A. Alvarez-Garcia. 2024-04-22. Integration of first-order ODEs by Jacobi fields. https://arxiv.org/abs/2404.14352

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