Invariants associated with linear ordinary differential equations

TL;DR

This paper introduces a new method for identifying invariants of linear ordinary differential equations, analyzing their structure, and determining the invariants' exact number across different orders.

Contribution

It presents a novel approach to find invariants and structure groups of linear ODEs, including a comparative study and application to various orders.

Findings

Developed a new method for invariants of linear ODEs

Determined the structure invariance group for arbitrary order

Identified the exact number of invariants for these equations

Abstract

We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next, the method is used to obtain the invariants of low order linear ordinary differential equations, and the structure invariance group for an arbitrary order of these equations. Other properties of these equations are also discussed, including the exact number of their invariants.