Linear Differential Equations: Homogeneous Case

This lecture covers linear ordinary differential equations of first order, focusing on homogeneous equations. The instructor defines an ordinary linear differential equation and explains the concept of homogeneity. Solutions to homogeneous equations can be combined linearly, and the lecture explores how to find these solutions. The instructor demonstrates the process step by step, showing how to isolate the unknown function in the equation. The lecture concludes by presenting a theorem that characterizes the unique solution to a homogeneous linear differential equation with a given initial condition. Various examples and demonstrations are provided throughout the lecture.