Liouvillian Solutions of Algebraic Ordinary Differential Equations of Order One of Genus Zero

作     者：NGUYEN Tri Dat NGO Lam Xuan Chau NGUYEN Tri Dat;NGO Lam Xuan Chau

作者机构：Faculty of Basic ScienceHo Chi Minh City University of TransportHo Chi Minh CityVietnam Department of Mathematics and StatisticsQuy Nhon UniversityQuy Nhon CityVietnam 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2023年第36卷第2期

页      面：884-893页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant No.101.04-2017.312 

主　　题：Algebraic ordinary differential equation autonomous differential equation Liouvillian solution rational algebraic curve rational parametrizations 

摘      要：This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general *** particular,let F(y,w)=0 be a rational algebraic curve over *** authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over ***,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus *** parametrizations of rational algebraic curves play an important role on this method.