Comparison of two classifications of a class of ODE's in the first case of intermediate degeneration

TL;DR

This paper compares two classifications of a specific class of second-order cubic ODEs in the intermediate degeneration case, establishing relationships between their invariants to unify different classification approaches.

Contribution

It provides a detailed comparison and correspondence between two classification schemes for second-order cubic ODEs in the intermediate degeneration case.

Findings

Established correspondence between invariants of the two classifications.

Unified understanding of classification schemes for the specific ODE class.

Clarified the role of various invariants in the classification process.

Abstract

Two classifications of second order ODE's cubic with respect to the first order derivative are compared in the first case of intermediate degeneration. The correspondence of vectorial, pseudovectorial, scalar, and pseudoscalar invariants of the equations in this case is established.