Existence and Uniqueness of Solutions

This lecture covers the proof of the existence and uniqueness of solutions for a given differential equation. Starting with the definition of a locally Lipschitz function, the lecture progresses to demonstrate the continuity of the function and the application of the Cauchy-Lipschitz theorem. Through a series of definitions and examples, the lecture illustrates the concept of local Lipschitz continuity and its implications on the existence and uniqueness of solutions. The lecture concludes with the verification of hypotheses and the application of the fixed-point theorem.