Integration of first-order ODEs by Jacobi fields

2024/04/22 by Pan-Collantes, A. J., Alvarez-Garcia, J. A.
#Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.14352

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 Schrödinger-type equations is highlighted.

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