A particular solution of a higher-order non-homogeneous Cauchy-Euler equation

TL;DR

This paper introduces a novel method using atoms on discrete sets to find particular solutions for higher-order non-homogeneous Cauchy-Euler equations, including approximate solutions via approximate roots.

Contribution

It develops an advanced approach leveraging atoms on discrete sets to solve complex Cauchy-Euler equations, offering both exact and approximate solutions.

Findings

New concept of atoms on discrete sets introduced

Method provides exact particular solutions for Cauchy-Euler equations

Approximate solutions obtained using approximate roots

Abstract

In this paper we introduce a new concept of atoms on discrete sets to develop an advanced method to find a particular solution for higher-order non-homogeneous Cauchy-Euler equations. The proposed method provides also an approximate solution by using approximate roots for the characteristic polynomial of the Cauchy-Euler equation.