First-order Autonomous ODE's: Qualitative Methods, Applications
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.
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.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Notes - Notes and exercises written by Prof. Mattuck
- Supplementary Notes 1 - Chapter 5 Supplementary Notes written by Prof. Miller
- Supplementary Notes 2 - Chapter 6 Supplementary Notes written by Prof. Miller
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What is an autonomous differential equation?
- What is a logistic equation?
- How do you get qualitative information about solutions to ODEs without solving?
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Staff Review
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.
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