标题： 阿贝尔常微分方程：等价性和可积类 显示英文标题

标题： Abel ODEs: Equivalence and Integrable Classes

摘要： 根据不变量理论，对已知的可解非常数不变量阿贝尔微分方程进行了分类，并在文献中进行了介绍。还展示了一组新的可积类，这些类依赖于一个或没有参数，是通过对阿贝尔、刘维尔和阿佩尔工作的分析得出的。开发了计算机代数例程，通过解决相关的等价问题来求解这些类别的ODE成员。 resulting library 允许在Maple符号计算环境中系统地求解阿贝尔型ODE。 显示英文摘要

摘要： A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of the works by Abel, Liouville and Appell, is also shown. Computer algebra routines were developed to solve ODEs members of these classes by solving their related equivalence problem. The resulting library permits a systematic solving of Abel type ODEs in the Maple symbolic computing environment.