First-order Substitution Methods: Bernouilli and Homogeneous ODE's

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Lesson Summary:

In this lecture, you will learn how to change variables in differential equations to reduce them to one of the cases that can be solved. The most common change of variables is called scaling, where you change the coordinates on the axes to stretch or contract them. Another important substitution method is the Bernoulli equation, where you divide through y to the nth power, no matter what n is. Then, you can make a new variable and turn the Bernoulli equation into a linear equation. By putting the p on the other side and solving it, you can arrive at the solution to the original problem.

Lesson Description:

First-order Substitution Methods: Bernouilli and Homogeneous ODE's -- Lecture 4. Learn how to change variables in differential equations.

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.