5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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 31E
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(a) Determine all critical points of the given system of equations.
(b) Find the corresponding linear system near each critical point.
(c) Find the eigenvalues of each linear system. What conclusions can you then draw about the
nonlinear system?
(d) Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them
in those cases where the linear system does not provide definite information about the nonlinear
system.
(e) Draw a sketch of, or describe in words, the basin of attraction of each asymptotically stable
critical point.
Transcribed Image Text:(a) Determine all critical points of the given system of equations. (b) Find the corresponding linear system near each critical point. (c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system? (d) Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them in those cases where the linear system does not provide definite information about the nonlinear system. (e) Draw a sketch of, or describe in words, the basin of attraction of each asymptotically stable critical point.
5. dx/dt = (4+x)(y-x), dy/dt = (10 − x) (y + x)
Transcribed Image Text:5. dx/dt = (4+x)(y-x), dy/dt = (10 − x) (y + x)
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