Matrix Systems of Differential Equations

This video describes how to write a high-order linear differential equation as a matrix system of first-order differential equations. This is a major step towards solving general ODEs using eigenvalues and eigenvectors, leveraging the full power of linear algebra.

Playlist:    • Engineering Math: Differential Equati...  
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This video was produced at the University of Washington

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0:00 Overview
1:54 Introduce New Variables
7:11 Writing as Matrix System of Equations
12:12 Summary and Takeaways
14:51 Eigenvalues of Matrix System are Roots of the Characteristic Polynomial
17:40 Example 3x3 Matrix System of ODEs