There exist several methods for computing exact solutions of algebraic differential equations. Most of the methods, however, do not ensure existence and uniqueness of the solutions and might fail after several steps, or are restricted to linear equations. The authors have presented in previous works a method to overcome this problem for autonomous first order algebraic ordinary differential equations and formal Puiseux series solutions and algebraic solutions. In the first case, all solutions can uniquely be represented by a sufficiently large truncation and in the latter case by its minimal polynomial. The main contribution of this paper is the implementation, in a MAPLE-package named FirstOrderSolve, of the algorithmic ideas presented therein. More precisely, all formal Puiseux series and algebraic solutions, including the generic and singular solutions, are computed and described uniquely. The computation strategy is to reduce the given differential equation to a simpler one by using local parametrizations and the already known degree bounds.

中文翻译：

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一阶自治AODE的Puiseux级数和代数解-一个MAPLE软件包

存在几种用于计算代数微分方程的精确解的方法。但是，大多数方法不能确保解的存在性和唯一性，并且可能在几个步骤后失败，或者仅限于线性方程式。作者在先前的工作中提出了一种方法，可以解决一阶自治代数常微分方程以及形式化Puiseux级数解和代数解的问题。在第一种情况下，所有解都可以唯一地由足够大的截断表示，在后一种情况下，可以由其最小多项式表示。本文的主要贡献是在一个名为FirstOrderSolve的MAPLE程序包中实现了其中提出的算法思想。更确切地说，所有正式的Puiseux系列和代数解决方案，包括通用解和奇异解在内的所有元素都可以唯一地计算和描述。该计算策略是通过使用局部参数化和已知的度界将给定的微分方程简化为一个简单的方程。