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Draw a direction field for the differential equation y'= -y(5 Based on the direction field, determine the behavior of y as If this behavior depends on the initial value of y at t = 0, de his dependency.

Draw a direction field for the differential equation y'= -y(5 Based on the direction field, determine the behavior of y as If this behavior depends on the initial value of y at t = 0, de his dependency.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. The two equilibrium solutions are y(t) = 0 and y(t) = 5 Solutions with initial values greater than 5 decrease toward the solution y(t) = 0. Solutions with initial values between 0 and 5 increase toward the solution y(t) X = X Solutions with initial values less than 0 decrease toward the solution y(t) = 0. X
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 → ∞o. If this behavior depends on the initial value of y at t = 0, describe this dependency. The two equilibrium solutions are y(t) = 0 and y(t) = 5 Solutions with initial values greater than 5 decrease toward the solution y(t) = 0. Solutions with initial values between 0 and 5 increase toward the solution y(t) X = X Solutions with initial values less than 0 decrease toward the solution y(t) = 0. X
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