Primer on Solving Ordinary Differential Equations (CHAPTER 08.01)
Exact Solution of 2nd order ODE with Fixed Constants: Repeated Real Roots of Characteristic Equation
Summary
Learn how you can find the exact solution of a 2nd order ODE (with Fixed Constants) by using the classical solution technique by finding the homogeneous and particular parts. In this example, the roots of the characteristic equation are real and repeated.
Learning Objective
After watching this video, you will refresh your pre-requisite knowledge of how to solve a second-order ordinary differential equation with fixed constants by using classical solution techniques. In this case, the characteristic equation of the homogeneous part of the solution has repeated roots. This is required to find the true error in the numerical solution of ordinary differential equations.
Transcript
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Annotated Slides
All Videos for this Topic
Exact Solution of 1st order ODE [YOUTUBE6:48]
Exact Solution of 1st order ODE: Another Example [YOUTUBE7:37]
Exact Solution of 2nd order ODE: Distinct Roots of Characteristic Equation [YOUTUBE 8:50]
Exact Solution of 2nd order ODE: Repeated Roots of Characteristic Equation [YOUTUBE 8:41]
Exact Solution of 2nd order ODE: Complex Roots of Characteristic Equation [YOUTUBE 9:34]
Complete Resources
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