Study of Ordinary Differential Equations and Applications

• Grant number: 24/21605-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Vinícius Lourenço da Rocha
• Grantee: Letícia Cerqueira de Assunção
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

In this scientific initiation project, we will study the introductory theory of Ordinary Differential Equations (ODEs). For first-order equations, we will address some of the main differential equations, such as the homogeneous, autonomous, exact, linear, Bernoulli, Ricatti and Clairaut equations. In addition, we will see some methods of solving these equations, such as the separable variables, substitution and Picard methods. For higher-order equations, we will study the fundamental set of solutions and also the methods for solving homogeneous linear equations with constant coefficients and the methods of undetermined coefficients and variation of parameters. Finally, we will address differential equations with variable coefficients and the Laplace Transform, as well as some of its main applications.