4.1 Differential Equations

In this lesson, you will learn about differential equations.

Lesson Objectives

  • Recognize differential equations and identify the order of a differential equation.
  • Verify that a given function is a solution to a given differential equation.
  • Given a basic differential equation, find the general solution using integration and find the particular solution when given an initial value.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

  1. YouTube video: What is a differential equation?
  2. YouTube video:Differential Equations – Basic idea of what it means to be a solution
  3. YouTube video:Basic Differential Equation with an Initial Condition

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

  1. Differential Equation  – definition, the order of a differential equation, initial conditions, initial value problem, general (and actual, implicit/explicit) solution to a differential equation – up to example 6
  2. Solving Differential Equations  – up to example 6 (examples with detailed answers provided)

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

  1. Solve Simple Differential Equations
  2. 5.1 Antiderivatives: Exercises  Do problems #11 – 15.

Additional Resources

Below are additional resources that help reinforce the content for this module.

  1. Differential Equations
  2. MathHelp Notebook on Differential Equations  (up to “direct integration” for now)