Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software
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. This work was carried out with the objective of analyzing the soluti...
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| Format: | Article |
| Language: | English |
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Centro Latinoamericano de Estudios en Informática
2025-08-01
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| Series: | CLEI Electronic Journal |
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| Online Access: | https://clei.org/cleiej/index.php/cleiej/article/view/689 |
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| author | Luis_Jaime Collantes_Santisteban Alberto Hananel Samuel Collantes Rosa Gonzales |
| author_facet | Luis_Jaime Collantes_Santisteban Alberto Hananel Samuel Collantes Rosa Gonzales |
| author_sort | Luis_Jaime Collantes_Santisteban |
| collection | DOAJ |
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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.
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.
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| format | Article |
| id | doaj-art-d01433e3877d44d9b9a0b7acf5d9a34c |
| institution | Matheson Library |
| issn | 0717-5000 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Centro Latinoamericano de Estudios en Informática |
| record_format | Article |
| series | CLEI Electronic Journal |
| spelling | doaj-art-d01433e3877d44d9b9a0b7acf5d9a34c2025-08-03T14:27:42ZengCentro Latinoamericano de Estudios en InformáticaCLEI Electronic Journal0717-50002025-08-0128410.19153/cleiej.28.4.1Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical SoftwareLuis_Jaime Collantes_Santisteban0Alberto Hananel1Samuel Collantes2Rosa Gonzales3Universidad Nacional Pedro Ruiz GalloUniversidad Nacional Pedro Ruiz GalloUniversidad Nacional Pedro Ruiz GalloUniversidad Nacional Pedro Ruiz Gallo 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. 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. https://clei.org/cleiej/index.php/cleiej/article/view/689Ordinary Differential EquationsMathematical SoftwareMapleGeometric and Numerical Analysis |
| spellingShingle | Luis_Jaime Collantes_Santisteban Alberto Hananel Samuel Collantes Rosa Gonzales Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software CLEI Electronic Journal Ordinary Differential Equations Mathematical Software Maple Geometric and Numerical Analysis |
| title | Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software |
| title_full | Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software |
| title_fullStr | Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software |
| title_full_unstemmed | Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software |
| title_short | Qualitative and Quantitative Approach to Ordinary Differential Equations through Mathematical Software |
| title_sort | qualitative and quantitative approach to ordinary differential equations through mathematical software |
| topic | Ordinary Differential Equations Mathematical Software Maple Geometric and Numerical Analysis |
| url | https://clei.org/cleiej/index.php/cleiej/article/view/689 |
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