Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

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PRIMER ON SOLVING ORDINARY DIFFERENTIAL EQUATIONS (CHAPTER 08.01)

 

Exact Solution

2nd Order Ordinary Differential Equations with Fixed Constants

Repeated Roots of Characteristic Equation

 

By Autar Kaw



TOPIC DESCRIPTION
 

Learn how you can find the exact solution of a 2nd order differential equation (with fixed constants) by using the classical solution technique (homogeneous and particular parts).

This video gives you an example of finding the exact solution of a second order differential equation with fixed constants by using the classical solution technique.  The roots of the characteristic equation are repeated.


ALL VIDEOS FOR THIS TOPIC
 

Exact Solution of 1st order ODE [YOUTUBE 6:48] [TRANSCRIPT]

Exact Solution of 1st order ODE: Another Example [YOUTUBE 7:37] [TRANSCRIPT]

Exact Solution of 2nd order ODE: Distinct Roots of Characteristic Equation [YOUTUBE  8:50] [TRANSCRIPT] 

Exact Solution of 2nd order ODE: Repeated Roots of Characteristic Equation [YOUTUBE  8:41] [TRANSCRIPT]

Exact Solution of 2nd order ODE: Complex Roots of Characteristic Equation [YOUTUBE  9:34] [TRANSCRIPT]


COMPLETE RESOURCES
  Get in one place the following: a textbook chapter, individual YouTube lecture videos, and multiple-choice questions on Primer on ODE.

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

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