This is an actual classroom lecture. This is the very first day of class in Differential Equations. We covered most of Chapter 1 which is mainly definitions, terminology, and initial value problems. Just tons of theory here.
Here is the book for the lectures https://amzn.to/4ajOMyW (affiliate link).

There are lots of notes and tons of definitions in this lecture.

Summary of Some of the Topics
Definition of a Differential Equation
Motivation for Differential Equations
Types of Differential Equations
Order of a Differential Equation
Linear versus Nonlinear Differential Equations
Solutions to Differential Equations
One parameter families and two parameter families of solutions
Particular Solutions
Explicit versus implicit solutions
The trivial solution
The General solution
Singular solutions
The interval of definition
Initial Value problems


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