Ordinary Linear Differential Equations

This lecture covers the solution of second-order linear ordinary differential equations with constant coefficients, focusing on finding the general solution by combining the homogeneous solution with a particular solution. The process involves identifying the form of the particular solution based on the type of forcing function, such as polynomials or trigonometric functions. Examples are provided to illustrate the application of the method, including finding solutions for forced harmonic oscillators. The lecture emphasizes the importance of determining the constants in the general solution using initial conditions, leading to a complete understanding of the differential equations.