求二阶有理常微分方程的初等首次积分
Finding Elementary First Integrals for Rational Second Order Ordinary Differential Equations
摘要：
本文给出了求二阶有理常微分方程初等首次积分的一个算法。在\cite{PS2}中，我们提出了处理SOODE的第一种算法方法，介绍了目前工作的基础。在\cite{royal}中，作者使用这些结果，并开发了一种方法来处理SOODE和分类。我们目前的算法是基于一个更坚实的理论基础（许多定理），并涵盖了更广泛的家庭SOODE比以前，因为我们不工作与限制的Anonymous。此外，我们目前的方法允许一个简单的可积性分析的SOODE和更快的实际计算。
英文摘要：
Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In \cite{PS2}, we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the present work. In \cite{royal}, the authors used these results and developed a method to deal with SOODEs and a classification of those. Our present algorithm is based on a much more solid theoretical basis (many theorems are presented) and covers a much broader family of SOODEs than before since we do not work with restricted ansatz. Furthermore, our present approach allows for an easy integrability analysis of SOODEs and much faster actual calculations.
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