For the system: = y(2+x – x²) and %3D (2 + х)(у — х) dt a. Find all the critical points. b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable.

For the system: = y(2+x – x²) and %3D (2 + х)(у — х) dt a. Find all the critical points. b. Plot the phase portrait and the direction field, and determine whether each critical point is stable, asymptotically stable, or unstable.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 35E

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Question

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please help immediately

dx
dy
For the system: = y(2 + x – x²) and
:= (2 + x)(y – x)
dt
dt
a. Find all the critical points.
b. Plot the phase portrait and the direction field, and determine whether each critical point is stable,
asymptotically stable, or unstable.
c. Describe the basin of attraction for each asymptotically stable critical point.

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