Linear Differential Equations: Methods and Solutions

This lecture focuses on linear ordinary differential equations (ODEs) of the first order. The instructor discusses the general form of these equations and introduces methods for solving them, including separation of variables and the method of undetermined coefficients. The lecture emphasizes the importance of identifying whether an equation is homogeneous or inhomogeneous, providing examples to illustrate these concepts. The instructor explains how to derive solutions for specific equations, demonstrating the process step-by-step. The lecture also covers the significance of the linearity of the equations and how it relates to vector spaces. Throughout the session, the instructor engages with students, encouraging questions and clarifying complex points. By the end of the lecture, students gain a comprehensive understanding of how to approach and solve first-order linear differential equations, preparing them for more advanced topics in differential equations.