The particular solutions of some types of Euler-Cauchy ODE using the differential transform method

Volume 12, Issue 3, pp 146--151 http://dx.doi.org/10.22436/jnsa.012.03.02

Publication Date: November 30, 2018 Submission Date: July 21, 2018 Revision Date: August 09, 2018 Accteptance Date: September 22, 2018

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Authors

Meshari Alesemi - Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia. M. A. El-Moneam - Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia. Bader S. Bader - Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia. E. S. Aly - Mathematics Department, Faculty of Science, Jazan University, Jazan, Kingdom of Saudi Arabia.

Abstract

In this paper, we apply the differential transform method to find the particular solutions of some types of Euler-Cauchy ordinary differential equations. The first model is a special case of the nonhomogeneous \(n^{\rm th}\) order ordinary differential equations of Euler-Cauchy equation. The second model under consideration in this paper is the nonhomogeneous second order differential equation of Euler-Cauchy equation with a bulge function. This study showed that this method is powerful and efficient in finding the particular solution for Euler-Cauchy ODE and capable of reducing the size of calculations comparing with other methods.

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Keywords

• Differential equations
• differential transform method
• Euler-Cauchy equations

MSC

•  65L05

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