Separable differential equations

In this video we define differential equations as equations involving a function and its derivatives, and the solution of a differential equation is the function that satisfies the differential equation. We look at the most basic type of a differential equation: the separable differential equation.

Chapters:

00:00 Introduction to differential equations
00:22 Definition of differential equations
00:43 Terms: Order of a differential equation
01:11 Terms: Solution of a differential equation
01:34 Terms: Separable differential equation
02:45 Example 1: First degree separable ODE
04:25 Example 1: Checking if the solution satisfies the equation
05:29 Example 1: Visualizing the family of solutions for the ODE
05:56 Example 2: Second degree separable ODE
06:43 Example 2: Writing the second derivative as the derivative of the first derivative
07:45 Example 3: Second degree separable ODE of trigonometric functions
08:24 Example 3: Using the substitution method
09:26 Example 4: Finding the particular solution of an ODE

This video is part of a lesson series in Integral #Calculus for my Grade 12 students in the Philippine Science High School Main Campus.