Existence and Uniqueness of Local Solutions

This lecture covers the proof of existence and uniqueness of local solutions for a Cauchy problem with separable variables. The instructor demonstrates the process step by step, showing how to find a local solution that is unique in a certain sense. The lecture also delves into the resolution of the Ordinary Differential Equation (ODE) using a chosen interval. Various mathematical concepts such as continuous functions, integrals, and derivatives are applied to establish the existence and uniqueness of solutions. The importance of factor integrants in determining solutions is highlighted, along with practical examples to illustrate the theoretical concepts.