Homogeneous Linear Second-Order Differential Equations

This lecture covers the solution of homogeneous linear second-order differential equations with constant coefficients. Starting with the general form of the equation, the instructor explains the method of finding solutions using the characteristic polynomial. The lecture then delves into specific cases, such as when the characteristic polynomial has real roots or complex conjugate roots. The concept of the characteristic polynomial associated with the equation is thoroughly discussed, leading to the identification of independent solutions. The lecture concludes with a detailed explanation of the solutions in the context of different scenarios.