Reducing y″=F(x,y,y′) to first order
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摘要
Necessary and sufficient conditions for a second-order ODE to be reducible to first order are given explicitly. The reducible real analytic equations are parameterized in terms of three functions of one variable and two functions of two variables, arbitrarily chosen. Some examples and particular cases are also discussed.
论文关键词：Primary 34A05,Secondary 34A26,34C14,34C20,58A20,58H05,Complete integrability,Fibred automorphism,Jet bundle,Order reduction,Second-order ODE
论文评审过程：Received 1 December 2001, Revised 22 July 2002, Available online 3 April 2003.
论文官网地址：https://doi.org/10.1016/S0377-0427(02)00876-2
