Linear 2nd Order ODEs: Boundary Value Problems

This lecture covers linear 2nd order ordinary differential equations (ODEs) formulated as boundary value problems (BVPs). It explains how to determine unique solutions by imposing conditions at distinct points, known as Boundary Conditions (BCs). Different types of BCs, such as Dirichlet, Neumann, and Robin, are discussed, along with the concept of homogeneous BCs. The lecture also explores the existence and uniqueness of solutions to BVPs, contrasting them with initial value problems. Examples are provided to illustrate the application of BCs in solving ODEs, emphasizing the importance of the solvability condition for unique solutions.