Estudo das Equações Diferenciais Ordinárias de primeira e segunda ordem e aplicações.

Abstract

This work presents a study on ordinary differential equations, where initially a little about the emergence and study of these equations is presented, as well as the leading names that gave their contributions to their development. Bibliographic research was carried out on first and second-order ordinary differential equations, where we present their main definitions: classification as to type, order, and linearity, the existence of solution, initial value problems, and the main methods to find solutions for these types of equations. As an application, we did a study on Newton’s Law of Cooling and presented a problem with application in criminal expertise. We also work with the spring-mass system modeled through a second-order differential equation, focusing on the damped mass-spring system. We present a problem that involves the three possible types of the damped motion: super damped, critically damped, and undamped. We then realized the importance of studying Differential Equations not only for mathematics but also for other areas of knowledge, since it allows modeling different situations studied by these areas.