Comparison of two classifications of a class of ODE's in the case of general position

2017/04/17 by Руслан Шарипов, Sharipov, Ruslan
Mathematics · #34A26 #34A34 #34C14 #34C20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1704.05022

openalex publication_date 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the case of general position, which is common for both classifications. The correspondence of vectorial, pseudovectorial, scalar, and pseudoscalar invariants is established.

Citations

• Course of differential geometry
• On the point transformations for the equation y''= P + 3Qy' + 3Ry'² + Sy'³
• Effective procedure of point-classification for the equation y'' = P + 3 Q y' + 3 R y'² + S y'³

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• On invariants of second-order ordinary differential equations y''=f(x,y,y') via point transformations
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