Draw a direction field for the differential equation y' = −y(5 - 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 5 Choose one ▾ Solutions with initial values between 0 and 5 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(5 - 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 5
Choose one ▾
Solutions with initial values between 0 and 5
Choose one ▾
Transcribed Image Text:Draw a direction field for the differential equation y'= -y(5 - 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 5 Choose one ▾ Solutions with initial values between 0 and 5 Choose one ▾
Solutions with initial values greater than 5
Choose one ▾
Solutions with initial values between 0 and 5
Choose one ▾
Solutions with initial values less than 0
Choose one
Transcribed Image Text:Solutions with initial values greater than 5 Choose one ▾ Solutions with initial values between 0 and 5 Choose one ▾ Solutions with initial values less than 0 Choose one
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