a.Draw a direction field and describe how solutions seem to behave. b.Find the critical points. 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. e.Draw a phase portrait for the system. f.Determine the limiting behavior of x and y as t → ∞. g.Interpret the results in terms of the populations of the two species. 1.dx/dt=x(1.5−0.5y)dy/dt=y(−0.5+x)

a.Draw a direction field and describe how solutions seem to behave. b.Find the critical points. 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. e.Draw a phase portrait for the system. f.Determine the limiting behavior of x and y as t → ∞. g.Interpret the results in terms of the populations of the two species. 1.dx/dt=x(1.5−0.5y)dy/dt=y(−0.5+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 32E

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Question

a.Draw a direction field and describe how solutions seem to behave.

b.Find the critical points.

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.

e.Draw a phase portrait for the system.

f.Determine the limiting behavior of x and y as t → ∞.

g.Interpret the results in terms of the populations of the two species.

1.dx/dt=x(1.5−0.5y)dy/dt=y(−0.5+x)

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