First integrals and solutions for a class of third-order  nonlinear autonomous differential equations

Qian Liu; Yanxia Hu

doi:10.1216/rmj-2021-51-643

Abstract

A class of third-order nonlinear autonomous differential equations is analyzed and solved. The first integral method suitable for the third-order autonomous differential equation is introduced and the first integrals of the equation are obtained by this method. Besides this, the functional transformations and Lie group theory are used to solve the equation.

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Qian Liu. Yanxia Hu. "First integrals and solutions for a class of third-order nonlinear autonomous differential equations." Rocky Mountain J. Math. 51 (2) 643 - 656, April 2021. https://doi.org/10.1216/rmj.2021.51.643

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Received: 13 April 2020; Revised: 18 August 2020; Accepted: 20 August 2020; Published: April 2021

First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.643

Subjects:

Primary: 34A05 , 34A34

Keywords: Differential equation , first integral method , first integrals , solutions

Abstract

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