This lecture covers the analysis of second-order linear differential equations with constant coefficients in the inhomogeneous case. The instructor explains how to find a particular solution and then derive the general form of the solution. The lecture also discusses the variation of constants technique and demonstrates how to find solutions to the differential equation. Additionally, it explores the concept of the variation of constants and how it generates solutions. The lecture concludes with examples illustrating the application of the theory to real-world problems.