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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast → co. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y - 2)² O Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞o depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 0. y(10) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → co is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞o depends on initial value y(to): y(to) > 0:y(1)→ 2. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞o depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2:y(1)→ 2. y(to) < 0:y(1) diverges from y = 0. O a -a a 7 VA //a 7 1 7 I

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast → co. If this behavior depends on the initial value of y at t = 0, describe this dependency. y' = y(y - 2)² O Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞o depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 0. y(10) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(1) ast → co is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞o depends on initial value y(to): y(to) > 0:y(1)→ 2. y(to) < 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast →∞o depends on initial value y(to): y(to) > 2: y(1) diverges from y = 2. 0 < y(to) < 2:y(1)→ 2. y(to) < 0:y(1) diverges from y = 0. O a -a a 7 VA //a 7 1 7 I

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Draw a direction field for the given differential equation. 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. y' = y(y - 2)² Where a = 2. Equilibrium solutions: a y(t) = 0 and y(t) = 2. Behavior of y(t) as to depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 0. y(to) 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(t) as t→∞o is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(to): y(to) > 0: y(t)→ 2. y(to) < 0: y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) as t→∞o depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2:y(1)→ 2. y(to) < 0: y(1) diverges from y = 0. O O //a 117 27 1 7 F 1 737
Transcribed Image Text:Draw a direction field for the given differential equation. 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. y' = y(y - 2)² Where a = 2. Equilibrium solutions: a y(t) = 0 and y(t) = 2. Behavior of y(t) as to depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2: y(t) → 0. y(to) 0:y(1) diverges from y = 0. Where a = 2. Equilibrium solution: y(t) = 2. Behavior of y(t) as t→∞o is independent of initial value y(to): y(to) → 2 for all y(to). Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(1) ast → ∞ depends on initial value y(to): y(to) > 0: y(t)→ 2. y(to) < 0: y(1) diverges from y = 0. Where a = 2. Equilibrium solutions: y(t) = 0 and y(t) = 2. Behavior of y(t) as t→∞o depends on initial value y(to): y(to) > 2:y(1) diverges from y = 2. 0 < y(to) < 2:y(1)→ 2. y(to) < 0: y(1) diverges from y = 0. O O //a 117 27 1 7 F 1 737
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