4 videos in "SecondOrder Linear ODEs"

Solving Secondorder Linear ODE's with Constant Coefficients: The Three Cases

Theory of General Secondorder Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians

Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constantcoefficient ODEs

Finding Particular Solutions to Inhomogeneous ODEs: Operator and Solution Formulas Involving Exponentials
Finding Particular Solutions to Inhomogeneous ODEs: Operator and Solution Formulas Involving Exponentials
Finding Particular Solutions to Inhomogeneous ODEs: Operator and Solution Formulas Involving Exponentials
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Part of video series Differential Equations Course acquired through MIT OpenCourseWare
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 BYNCSA.
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More info at: http://ocw.mit.edu/terms
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Finding Particular Solutions to Inhomogeneous ODEs: Operator and Solution Formulas Involving Exponentials  Lecture 13. A spattering of formulas for finding particular solutions to ODEs.
 Lecture Notes  Lecture Notes
 Muddy Card Responses  Muddy Card Responses are explanations of topics that were confusing to students
 Notes  Notes and exercises written by Prof. Mattuck
 Supplementary Notes  Chapter 10 Supplementary Notes written by Prof. Miller
 Recitation Problems  Recitation Problems and classwork exercises
 Recitation Solutions  Recitation problem solutions
 What is an inhomogeneous ODE?
 What is a particular solutions to an ODE?
 What is the exponential input theorem?
 What is the exponential shift rule?
 How do you know if a is a single or a double root?
This is a very important lesson in exponential differential equations and oscillations of springs. Many solution formulas and their proofs are presented in the lesson as well. A bit of a complicated and very theoretical lecture with many formulas represented.