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General Solutions of Some Complex Third-order Differential Equations
American Journal of Applied Mathematics
Volume 8, Issue 6, December 2020, Pages: 319-326
Received: Nov. 10, 2020; Accepted: Nov. 26, 2020; Published: Dec. 8, 2020
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Rong Liao, School of Mathematical Sciences, South China Normal University, Guangzhou, China; Lihu Experimental School of Shenzhen University Town, Shenzhen, China
Zhibo Huang, School of Mathematical Sciences, South China Normal University, Guangzhou, China
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According to the Nevanlinna theory, many researches have undertaken the behaviors of meromorphic solutions of complex ordinary differential equations (ODEs). Most of these researches have concentrated on the value distribution and growth of meromorphic solutions of ODEs. However, the existence of a meromorphic general solution is often used as a way to identify equations that are integrable. Especially, the existence of global meromorphic solutions of differential equation with entire coefficient can be settled, resulting in the characterization of Schwarzian derivatives. This is concerning with the linearly independent solutions of linear differential equations . The purpose of this present paper is to find explicit solutions of differential equation in terms of finite combinations of known functions, that is, we use local series methods and reduction of order to solve all linearly independent solutions of some third-order ODEs with entire coefficient in the neighborhood of z0.
Ordinary Differential Equation, Local Series Method, Linearly Independent, Meromorphic General Solution
To cite this article
Rong Liao, Zhibo Huang, General Solutions of Some Complex Third-order Differential Equations, American Journal of Applied Mathematics. Vol. 8, No. 6, 2020, pp. 319-326. doi: 10.11648/j.ajam.20200806.14
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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