The general solution of the non-homogeneous Euler–Cauchy operator-differential equation with Neumann boundary conditions using the Laplace transform

Many researchers are interested in topics related to solutions of differential equations with variable coefficients. Here for the first time, we study the nonhomogeneous second-order Euler–Cauchy operator-differential equation. In this paper, we apply the Laplace transform method to find the general...

Full description

Saved in:
Bibliographic Details
Published in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters 2024-03, Vol.9, p.100613, Article 100613
Main Authors: Ahmed, Abdel Baset I., Labeeb, Mohamed A.
Format: Article
Language:English
Subjects:
Euler–Cauchy equations
Laplace transform
Neumann boundary conditions
Operator-differential equation
Self-adjoint operator
Variable coefficients
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Many researchers are interested in topics related to solutions of differential equations with variable coefficients. Here for the first time, we study the nonhomogeneous second-order Euler–Cauchy operator-differential equation. In this paper, we apply the Laplace transform method to find the general solution of the Euler–Cauchy equation with Neumann boundary conditions. We show that this method is powerful in finding the general solution of the Euler–Cauchy equation in terms of generalized exponential functions.
ISSN:2666-8181
2666-8181
DOI:10.1016/j.padiff.2023.100613