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

Volume 12, Issue 3, pp 146--151
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.

### Share and Cite

##### ISRP Style

Meshari Alesemi, M. A. El-Moneam, Bader S. Bader, E. S. Aly, The particular solutions of some types of Euler-Cauchy ODE using the differential transform method, Journal of Nonlinear Sciences and Applications, 12 (2019), no. 3, 146--151

##### AMA Style

Alesemi Meshari, El-Moneam M. A., Bader Bader S., Aly E. S., The particular solutions of some types of Euler-Cauchy ODE using the differential transform method. J. Nonlinear Sci. Appl. (2019); 12(3):146--151

##### Chicago/Turabian Style

Alesemi, Meshari, El-Moneam, M. A., Bader, Bader S., Aly, E. S.. "The particular solutions of some types of Euler-Cauchy ODE using the differential transform method." Journal of Nonlinear Sciences and Applications, 12, no. 3 (2019): 146--151

### Keywords

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

•  65L05

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