Classification of $n-$th order linear ODEs up to projective transformations

TL;DR

This paper discusses classifying nth order linear ordinary differential equations up to projective transformations by reducing them to Laguerre-Forsyth form using a method developed by V.A. Yumaguzhin.

Contribution

It introduces a classification approach for nth order linear ODEs based on projective transformations and reduction to Laguerre-Forsyth form, building on Yumaguzhin's method.

Findings

Effective classification scheme for nth order linear ODEs.

Reduction to Laguerre-Forsyth form simplifies analysis.

Provides a systematic approach for transformations.

Abstract

Classification of $n-$th $(n\geq2)$ order linear ODEs is considered. The equation reduced to \textit{Laguerre-Forsyth} form by a point transformation then, the other calculations would have done on this form. This method is due to \textit{V.A. Yumaguzhin}.