4.3 Other Elementary Differential Equations

In this lesson, you will learn about other elementary differential equations.

Lesson Objectives

  • Identify and solve separable first-order differential equations.
  • Identify and solve first order linear differential equations with constant coefficients.
  • Model and solve applications involving first-order linear and separable differential equations.

Lesson Content

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

  1. YouTube videos: Separable Differential Equations
    Part 1:

    Part 2:

  2. YouTube video: First Order Differential Equations
  3. YouTube video: First Order Linear Differential Equations
  4. YouTube videos: Solving Separable First Order Differential Equations
    Example 1:

    Example 2:

  5. YouTube video: Logistic Differential Equation

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. Separable Equations
  2. Separable First Order Differential Equations
  3. Notes on Differential Equations  – First order linear differential equation (separable equation, general first order equations, initial value problems)
  4. Section 8.3- First Order Linear Differential Equations
  5. Logistic Growth Model
  6. Logistic Growth Model – Part 2: Equilibria
  7. Logistic Growth Model – Part 3: Infection Points and Concavity
  8. Logistic Growth Model – Part 4: Symbolic Solutions
  9. Logistic Growth Model – Part 5: Fitting a Logistic Model to Data, I
  10. Logistic Growth Model – Part 6: Fitting a Logistic Model to Data, II
  11. Logistic Growth Model – Part 7: Summary

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. Constant Coefficient Linear Differential Equations  (problems 1-6, with solutions provided)
  2. Quiz 9: First Order Linear Differential Equations
  3. Population Dynamics: Example 1

Additional Resources

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

  1. Solving First Order Differential Equations: Separable and Linear Equations
  2. First-Order Linear Differential Equations
  3. Linear First-order Differential Equations with Constant Coefficients
  4. Logistic Growth Model