Draw a direction field for the differential equation y'= -y(8-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 1 y(t) = and y(t) Solutions with initial values greater than 8 Choose one Solutions with initial values between 0 and 8 Choose one Solutions with initial values less than 0 Choose one

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Draw a direction field for the differential equation y'= -y(8- 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
1
y(t) =
and y(t):
=
Solutions with initial values greater than 8
Choose one
Solutions with initial values between 0 and 8
Choose one
Solutions with initial values less than 0
Choose one
Transcribed Image Text:Draw a direction field for the differential equation y'= -y(8- 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 1 y(t) = and y(t): = Solutions with initial values greater than 8 Choose one Solutions with initial values between 0 and 8 Choose one Solutions with initial values less than 0 Choose one
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