Homogeneous Differential Equations

This lecture covers the solution of homogeneous differential equations with the method of polynomials. Starting with the associated homogeneous problem, the instructor demonstrates the step-by-step process of finding solutions using polynomials. Emphasis is placed on determining the coefficients and constants in the solutions. The lecture progresses to discuss the inhomogeneous problem and the general solution, highlighting the importance of polynomial degrees in the solutions. Various examples are provided to illustrate the application of the method in different scenarios, leading to a comprehensive understanding of solving homogeneous differential equations.