Explicit Meromorphic Solutions of a Second Order Briot–Bouquet Differential Equation
摘要
In this paper, a special second-order Briot–Bouquet differential equation is studied. We construct explicit meromorphic solutions by the Kowalevski–Gambier method and a careful discussion. How we take into account the corresponding series at zeros, as opposed to the Laurent series at poles. This method is also useful for the study of many other non-linear differential equations.