Higher-Order ODE - 3.1 - Theory of Linear Equations - Part 1 of 2

In the following two segments, we discuss various common concepts we need when solving higher-order differential equations. In the first part of the series, we cover the initial value problem, boundary value problem, existence and uniqueness of a solution, homogenous equation, differential operator, nth order differential operator (L), and superposition principle.

Errata: at timestamp 1:10, the last term on the left-hand side should read a_0(x) y, y is missing. This material is based upon work supported by the National Science Foundation under Grant No. 2019664. Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

[saadetozer]

right before the equality, the last term must be a_0(x) y, not just a_0, otherwise it would not be an nth order linear ode.