General Solution of Homogeneous Second Order Linear Differential Equations

This lecture covers the general solution of homogeneous second-order linear differential equations with constant coefficients, the existence and uniqueness of a solution with two initial conditions, linearly independent solutions, and how to find a linearly independent solution from a nontrivial solution of a homogeneous second-order linear differential equation. The lecture also discusses homogeneous second-order linear differential equations with constant coefficients, finding solutions using exponential functions, and the concept of linear independence of solutions.