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.
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