Linear Homogeneous Second Order Equations

This lecture covers linear homogeneous second order differential equations of the form y'' + p(t)y' + q(t)y = 0, where p and q are continuous functions. It explains the concepts of linear, homogeneous, and second order equations, as well as the lemma stating that linear combinations of solutions are also solutions. The lecture also discusses the Wronskian, the uniqueness of solutions, and the relationship between linearly independent solutions. Furthermore, it explores inhomogeneous second order equations and how to find solutions using known solutions. The session concludes by highlighting the relationship between solutions of inhomogeneous and homogeneous equations.