4 videos in "Second-Order Linear ODEs"
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Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases
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Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians
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Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constant-coefficient ODEs
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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 BY-NC-SA.
More info at: http://ocw.mit.edu/terms
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.
