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Draw a direction field for the differential equation y' = -y(1 – 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) %3D and y(t) Solutions with initial values greater than 1 Choose one Solutions with initial values between 0 and 1 Choose one Solutions with initial values less than 0 Choose one

Draw a direction field for the differential equation y' = -y(1 – 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) %3D and y(t) Solutions with initial values greater than 1 Choose one Solutions with initial values between 0 and 1 Choose one Solutions with initial values less than 0 Choose one

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(1 – 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. %3D The two equilibrium solutions are y(t) %3D and y(t) Solutions with initial values greater than 1 Choose one Solutions with initial values between 0 and 1 Choose one Solutions with initial values less than 0 Choose one
Transcribed Image Text:Draw a direction field for the differential equation y' = -y(1 – 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. %3D The two equilibrium solutions are y(t) %3D and y(t) Solutions with initial values greater than 1 Choose one Solutions with initial values between 0 and 1 Choose one Solutions with initial values less than 0 Choose one
Choose one diverge from the solution y(t) = 0. decrease toward the solution y(t) = 0. decrease toward the solution y(t) = 1. increase toward the solution y(t) = diverge from the solution y(t) = 1. increase toward the solution y(t) =
Transcribed Image Text:Choose one diverge from the solution y(t) = 0. decrease toward the solution y(t) = 0. decrease toward the solution y(t) = 1. increase toward the solution y(t) = diverge from the solution y(t) = 1. increase toward the solution y(t) =
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