Uma abordagem das Equações Diferenciais Ordinárias aplicadas em circuitos elétricos

Abstract

This work aims to present an approach to Ordinary Differential Equations (ODEs) applied to electrical circuits. Initially, a historical overview of the development of differential equations and electromagnetism is provided, highlighting contributions from scientists such as Newton, Leibniz, Euler, and Maxwell. The study delves into the classification of differential equations regarding type, order, and linearity, in addition to presenting solution methods such as separation of variables, integrating factor, and the use of the characteristic equation. In the applied section, elements of electrical circuits (resistors, capacitors, inductors) and their relationships with ODEs are analyzed, demonstrating how mathematical modeling contributes to understanding and solving physical and technological problems. The research adopts a bibliographic and exploratory approach, based on classical and contemporary authors.