Draw a direction field for the differential equation y=-y(3-y). Based on the direction field, determine the behavior of y as t→ ∞. If this behavior depends on the initial value of y at t= 0, describe this dependency. The two equilibrium solutions are y(t) = and y(t) Solutions with initial values greater than 3 Choose one Solutions with initial values between 0 and 3 Choose one Solutions with initial values less than 0 Choose one

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Draw a direction field for the differential equation y=-y(3-y).
Based on the direction field, determine the behavior of y as t → ∞o.
If this behavior depends on the initial value of y at t = 0, describe
this dependency.
The two equilibrium solutions are
y(t) =
and y(t) =
Solutions with initial values greater than 3
Choose one
Solutions with initial values between 0 and 3
Choose one
Solutions with initial values less than 0
Choose one
Transcribed Image Text:Draw a direction field for the differential equation y=-y(3-y). Based on the direction field, determine the behavior of y as t → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. The two equilibrium solutions are y(t) = and y(t) = Solutions with initial values greater than 3 Choose one Solutions with initial values between 0 and 3 Choose one Solutions with initial values less than 0 Choose one
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