Ordinary Differential Equations: Second Order Linear Inhomogeneous

This lecture covers the resolution of second-order linear ordinary differential equations with constant coefficients and a source term. It includes examples such as damped harmonic oscillators and forced harmonic oscillators. The general solution involves finding the general solution of the homogeneous equation, a particular solution of the equation with a source term, and applying initial conditions. Specific methods for finding particular solutions based on the form of the source term are discussed, such as choosing solutions of the same form with adjusted coefficients. The lecture also explores characteristic equations, roots, and the general solutions for different scenarios.