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

TL;DR

This paper compares two classifications of a specific class of second-order cubic ODEs in general position, establishing the correspondence of their invariants to unify understanding of their structure.

Contribution

It provides a detailed comparison and correspondence between two existing classifications of second-order cubic ODEs in general position, clarifying their invariant structures.

Findings

Established correspondence of invariants between classifications

Unified understanding of ODE classification in general position

Clarified the structure of invariants for second-order cubic ODEs

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.