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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as / → 00. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = yy – 5)? Where a - 5. Equilibrium solution: y(1) = 5. Behavior of y(f) as / → co is independent of initial value y(to): y(to) → 5 for all y(to). Where a - 5. Equilibrium solutions: y(1) = 0 and y(1) = 5. Behavior of y(f) as f → co depends on initial value y(t0): y(10) > 0: y(t) → 5. y(10) < 0: y(1) diverges from y = 0.

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as / → 00. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = yy – 5)? Where a - 5. Equilibrium solution: y(1) = 5. Behavior of y(f) as / → co is independent of initial value y(to): y(to) → 5 for all y(to). Where a - 5. Equilibrium solutions: y(1) = 0 and y(1) = 5. Behavior of y(f) as f → co depends on initial value y(t0): y(10) > 0: y(t) → 5. y(10) < 0: y(1) diverges from y = 0.

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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Drawa 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 = yv – 5) Where a - 5. Equilibrium solution: y(1) = 5. Behavior of y(f) as t → co is independent of initial value y(to): y(to) → 5 for all y(to). a Where a - 5. Equilibrium solutions: y(1) = 0 and y(1) = 5. Behavior of y(t) as t → co depends on initial value y(to): y(1o) > 0: y(t) → 5. y(40) < 0: y(1) diverges from y = 0.
Transcribed Image Text:Drawa 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 = yv – 5) Where a - 5. Equilibrium solution: y(1) = 5. Behavior of y(f) as t → co is independent of initial value y(to): y(to) → 5 for all y(to). a Where a - 5. Equilibrium solutions: y(1) = 0 and y(1) = 5. Behavior of y(t) as t → co depends on initial value y(to): y(1o) > 0: y(t) → 5. y(40) < 0: y(1) diverges from y = 0.
Where a - 5. Equilibrium solutions: y(t) = 0 and y(t) = 5. Behavior of y(1) as t → o depends on initial value y(t0): y(10) > 5:y(1) diverges from y = 5. 0 < y(to) < 5:y(1) → 5. y(to) < 0: y(1) diverges from y = 0. Where a - 5. Equilibrium solutions: y(1) = 0 and y(t) = 5. Behavior of y(1) as t → o depends on initial value y(t0): y(to) > 5:y(1) diverges from y = 5. 0 < y(to) < 5:y(1) → 0. y(40) < 0: y(1) diverges from y = 0.
Transcribed Image Text:Where a - 5. Equilibrium solutions: y(t) = 0 and y(t) = 5. Behavior of y(1) as t → o depends on initial value y(t0): y(10) > 5:y(1) diverges from y = 5. 0 < y(to) < 5:y(1) → 5. y(to) < 0: y(1) diverges from y = 0. Where a - 5. Equilibrium solutions: y(1) = 0 and y(t) = 5. Behavior of y(1) as t → o depends on initial value y(t0): y(to) > 5:y(1) diverges from y = 5. 0 < y(to) < 5:y(1) → 0. y(40) < 0: y(1) diverges from y = 0.
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