Differential Equations: General Solutions and Methods

This lecture focuses on solving differential equations, particularly linear inhomogeneous equations. The instructor discusses the general solution of such equations, emphasizing the relationship between the homogeneous and inhomogeneous parts. The lecture begins with a review of the types of equations being studied, followed by a detailed explanation of how to find the general solution. The instructor illustrates the process of finding a primitive function and how it relates to the solution of the differential equation. The method of variation of constants is introduced as a technique to solve these equations. The instructor provides examples to demonstrate how to apply this method effectively. Throughout the lecture, the importance of understanding the underlying principles of differential equations is highlighted, along with practical tips for solving them. The session concludes with a discussion on the significance of finding particular solutions and the role of initial conditions in determining the constants in the general solution.