First-order Autonomous ODE's: Qualitative Methods, Applications

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Taught by OCW
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Lesson Summary:

In this lesson, you will learn how to get useful information about solutions of a first-order autonomous ODE without actually solving the equation. By finding the critical points, you can draw the graph of f(y) and determine where it's positive or negative. This, in turn, tells you whether the solution is increasing or decreasing, giving you important qualitative information about its behavior. Using a simple example of a bank account with withdrawals, the lesson demonstrates how this method can be used to analyze the behavior of solutions without actually solving the equation.

Lesson Description:

First-order Autonomous ODE's: Qualitative Methods, Applications -- Lecture 5. Learn what solutions look like without solving the equation.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 26, 2008). License: Creative Commons BY-NC-SA.
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Additional Resources:
Questions answered by this video:
  • What is an autonomous differential equation?
  • What is a logistic equation?
  • How do you get qualitative information about solutions to ODEs without solving?
  • Staff Review

    • Currently 4.0/5 Stars.
    In this video, you will learn how to get qualitative information about solutions to ODEs without actually solving them. The information you learn in this lesson is very important to understanding solutions to differential equations. A good number of real-world problems are discussed in this video as well.