(c) For each critical point, find the corresponding linear system. Find the eigenvalues and eigenvectors of the linear system. Classify each critical point as to type, and determine whether it is asymptotically stable, stable, or unstable. (d) Sketch the trajectories in the neighborhood of each critical point.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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5. dx/dt = x(−1+2.5x -0.3y - x²), dy/dt = y(-1.5+ x)
Transcribed Image Text:5. dx/dt = x(−1+2.5x -0.3y - x²), dy/dt = y(-1.5+ x)
(c) For each critical point, find the corresponding linear system. Find the eigenvalues and
eigenvectors of the linear system. Classify each critical point as to type, and determine whether it is
asymptotically stable, stable, or unstable.
(d) Sketch the trajectories in the neighborhood of each critical point.
Transcribed Image Text:(c) For each critical point, find the corresponding linear system. Find the eigenvalues and eigenvectors of the linear system. Classify each critical point as to type, and determine whether it is asymptotically stable, stable, or unstable. (d) Sketch the trajectories in the neighborhood of each critical point.
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