Calculus Portal

Objective 1a: Separation of Variables

You will be able to solve differential equations by separating variables

Slope Fields and Separable Equations

In this introductory video, we review concepts from the previous lesson on slope fields and verifying a solution to a differential equation, and we begin to distinguish a differential equation that is separable from one that is not. Duration: 9:35

A Separation of Variables

Here, we will formally define a separable differential equation and demonstrate the technique of using separation to solve a first order differential equation. Don't forget your "plus C"! Duration: 12:11

Pro Techniques

When solving separable differential equations, some unique algebraic situations arise. This video seeks to provide a handful of pro techniques that will enable you to handle those situations, which we will put into practice on Example 3. Duration: 15:27

Examples 4 and 5

This video presents two more examples of solving first order differential equations by separating variables and then applies a couple of pro techniques to simplify our answers. Duration: 9:31

Examples 6 and 7

In Example 6, we learn to use the calculator to approximate the solution to a differential equation when no closed-form antiderivative can be found. Then in Example 7, we deal with absolute value once again to determine which of the two solutions to choose based on the position of our initial condition. Duration: 15:02