Implementation of Qualitative and Quantitative Methods in Ordinary Differential Equations using Maple Mathematical Software

The implementation of qualitative and quantitative methods in ordinary differential equations, in both its theoretical and applied parts, requires the use of mathematical software to achieve a modern approach with effectiveness in geometric and numerical analysis. The present work was carried out with the objective of analyzing the solution of mathematical problems related to first-order ordinary differential equations, qualitatively and quantitatively. For this, the Maple software was used, due to its powerful mathematical machine and great symbolic capacity, with an interface that makes it easy to analyze, explore, visualize and solve mathematical problems related to qualitative and quantitative theory of ordinary differential equations. First, specific features of Maple mathematical software that are useful for analyzing ordinary differential equations are identified. Then, first-order ordinary differential equations are analyzed and solved with Maple, considering existence, uniqueness, and stability of ordinary differential equations. A qualitative approach to the study of first-order ordinary differential equations is discussed, obtaining qualitative information about the solutions directly from the equation, without the use of a formula for the solution. In this work, worksheets have been built and developed in Maple that contain the solution to the problems posed in the attached data recording sheets, the same ones that appear in the literature with the names Problem Set A: Practice with Maple and Problem Set B: First Order Equations. Graphic and numerical representations are obtained that help carry out a convenient analysis and interpretation of the problems posed.