Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases
In this lesson, we learn how to solve second-order linear differential equations with constant coefficients. The basic method is to try y equals an exponential and find two solutions. There are three cases: the roots are real and unequal, the roots are complex conjugates, and the roots are real and equal. We use an example of a spring-mass system to show how to put in initial conditions and find the general solution.
Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases -- Lecture 9. Learn about second-order 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
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What is a second-order linear ODE?
- What is a real-world example of a second-order differential equation?
- How do you solve a second-order ODE?
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Staff Review
This lecture focuses on the study of linear second-order differential equations with constant coefficients. A physics problem with a spring, a mass, and forces is discussed and a second-order ODE is written. Also, second-order ODEs are solved in this lecture. A really useful lecture to watch in order to learn second-order differential equations.
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