Ordinary Differential Equations: Definitions and Solutions

This lecture covers the definitions and solutions of Ordinary Differential Equations (ODEs). It starts by introducing the concept of ODEs and their general form. The lecture explains the notation used for ODEs and the domain of the solution. It then delves into examples of ODEs, polynomial degrees, and autonomous solutions. The lecture also discusses the concept of maximal solutions and general solutions, along with specific examples to illustrate these concepts. Additionally, it explores the solution of Cauchy's problem and the verification of solutions. The lecture concludes with the resolution of ODEs with separate variables and informal currents.