Differential invariants and equivalence of ODEs y''=a³(x,y)y'³+a²(x,y)y'²+a¹(x,y)y'+a⁰(x,y)

2025/08/29 by Valeriy Yumaguzhin, Yumaguzhin, Valeriy A.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2508.21439

openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to ordinary differential equations of the form y''=a³(x,y)y'³+a²(x,y)y'²+a¹(x,y)y'+a⁰(x,y) The algebra of all differential invariants of point transformations is constructed for these equations in general position and the equivalence problem is solved for them.

Related

• Differential invariants of 2--order ODEs, I
• On the point transformations for the second order differential equations. I
• On invariants of second-order ordinary differential equations y''=f(x,y,y') via point transformations
• Invariants of third-order ordinary differential equations y'''=f(x,y,y',y'') via fiber preserving transformations
• Effective procedure of point-classification for the equation y'' = P + 3 Q y' + 3 R y'² + S y'³