First-order Substitution Methods: Bernouilli and Homogeneous ODE's
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.
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.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 3 Supplementary Notes written by Prof. Miller
- Problem Set 1 - Problem Set 1
- Problem Set 1 Solutions - Problem Set 1 Solutions
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What are the First-order Substitution Methods?
- What are Bernouilli ODEs?
- What are Homogeneous ODEs?
- What is scaling?
- What is direct substitution?
- What is inverse substitution?
- What is an integrating factor?
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Staff Review
This video talks about the change of variables and substitution to make an equation solvable. Also, scaling is discussed in various differential equations to change units, make unit dimensionless, or to reduce the number of or simplify constants in a function. Some examples are shown, and this video covers a lot of very important and intense differential equations topics.
