Ordinary Differential Equations: Definitions and Methods

This lecture covers the definitions and examples of ordinary differential equations, including terminology, order, and linear equations. It also explores methods of proof, such as proof by contrapositive and mathematical reasoning, illustrated with historical examples from Euclid. Additionally, it delves into solving Cauchy problems and differential equations with separated variables. The presentation emphasizes the importance of logical reasoning and the step-by-step process of deriving conclusions from axioms and previously established propositions.