Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs – A MAPLE Package

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