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This video analyzes 2×2 linear systems of ordinary differential equations with pairs of positive or negative real eigenvalues. It derives solutions using eigenvalues and eigenvectors and illustrates the resulting unstable source and stable sink in phase space.
Syllabus
Overview of sources and sinks
Writing the solution
Recap: How to compute matrix inverse
Drawing an unstable source in phase space
Drawing a stable sink in phase space
Taught by
Steve Brunton