Solutions of Non-Homogenous Linear Differential Equations

TL;DR

This paper investigates solutions of non-homogeneous linear differential equations with entire coefficients, providing a comprehensive characterization of all infinite order solutions under specific coefficient conditions.

Contribution

It offers a complete description of all infinite order solutions for such differential equations by imposing particular restrictions on the coefficients.

Findings

All non-trivial solutions of infinite order are characterized.

Conditions on coefficients are identified to obtain solutions.

The solutions are expressed explicitly under these conditions.

Abstract

This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots +a_1f'+a_0f=H(z)$, by restricting the conditions on coefficients.