Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software

Santisteban L.J.C.; Hananel A.; Santisteban S.C.; Gonzales R. · CLEI Eletronic Journal (CLEIej) (2025) · DOI: 10.19153/cleiej.28.4.1

Resumen

The implementation of qualitative and quantitative methods in Ordinary Differential Equations (ODEs) requires the use of mathematical software to achieve a modern approach with effectiveness in geometric and numerical analysis. The analysis of existence, uniqueness, and stability of differential equations is a difficult subject to address and understand without the necessary tools to understand the concepts involved and to visualize them graphically, geometrically, and numerically. This work was carried out with the objective of analyzing the solution of mathematical problems related to first-order ODEs. The Maple software was used, due to its great symbolic capacity, with an interface that makes it easy to analyze, explore, visualize and solve mathematical problems. First-order ODEs are analyzed and solved with Maple, considering existence, uniqueness, and stability. Also, a qualitative approach is discussed, obtaining qualitative information about the solutions directly from the equation, without the use of a formula for the solution. Worksheets have been built and developed in Maple containing the solution to some problems posed in the literature. Graphic and numerical representations are obtained that help carry out a convenient analysis and interpretation of the problems posed.

Instituciones: Universidad Nacional Pedro Ruiz Gallo