Homogeneous ODEs: Examples and Physics Applications

This lecture covers the solution to a homogeneous ordinary differential equation (ODE) with a continuous function p, providing all solutions to the ODE. It then explores a physics example involving a capacitor discharge circuit, discussing the voltage across the capacitor and the current in the circuit. The lecture also delves into finding functions satisfying specific conditions and analyzing the solutions to different types of ODEs. Finally, it examines the characteristics of exponential discharge in a capacitor and the solutions to ODEs on different intervals.