Group Classification of a family of second-order differential equations

2009/02/13 by J. C. Ndogmo, Ndogmo, J. C.
Computer Science · Mathematics · Physics and Astronomy · #34C20 #58J70 #76M60 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0902.2390

openalex publication_date 2009/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the group of equivalence transformations for equations of the form y''= A(x)y' + F(y), where A and F are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method of analysis, together with the equivalence transformations.

Related

• Equivalence for Differential Equations
• On dummy variables of structure-preserving transformations
• Complete Group Classification of Systems of Two Nonlinear Second-Order Ordinary Differential Equations of the Form \bf y^′′=\bf F(\bf y)
• Group Classification of Generalised Eikonal Equations
• Application of Group Analysis to Classification of Systems of Three Second-Order Ordinary Differential Equations