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Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y – 7 Where a = 7. Equilibrium solutions: 721 y(t) = 0 and y(t) = 7. Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 0: y(1) → 7. y(to) < 0: y(4) diverges from y = 0. Where a = 7. Equilibrium solution: ンン y(t) = 7. Behavior of y() as is independent of initial value y(to): y(10) 7 for all y(fo).

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y – 7 Where a = 7. Equilibrium solutions: 721 y(t) = 0 and y(t) = 7. Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 0: y(1) → 7. y(to) < 0: y(4) diverges from y = 0. Where a = 7. Equilibrium solution: ンン y(t) = 7. Behavior of y() as is independent of initial value y(to): y(10) 7 for all y(fo).

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 ast → o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y – 7 Where a = 7. Equilibrium solutions: y(1) = 0 and y(t) = 7. Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 0: y(1) → 7. y(to) < 0: y(1) diverges from v = 0. Where a = 7. Equilibrium solution: y(1) = 7. Behavior of y() as is independent of initial value y(to): y(to) 7 for all (ro ).
Transcribed Image Text:Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y ast → o. If this behavior depends on the initial value of y at t = 0, describe this dependency. y = y(y – 7 Where a = 7. Equilibrium solutions: y(1) = 0 and y(t) = 7. Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 0: y(1) → 7. y(to) < 0: y(1) diverges from v = 0. Where a = 7. Equilibrium solution: y(1) = 7. Behavior of y() as is independent of initial value y(to): y(to) 7 for all (ro ).
y(to) - 7 for all y(to). /? /// / / Where a = 7. Equilibrium solutions: y(t) = 0 and y(f) = 7. %3D I IER 7/ E Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 7: y(t) diverges from y = 7. 0 < y(to) < 7: y(t) → 7. y(to) < 0; y(1) diverges from y = 0. Where a = 7. Equilibrium solutions: y() = 0 and y(r) = 7. Behavior of y(t) as t → o depends on initial value y(to ): 555 y(to) > 7: y(1) diverges from y = 7. 0<y(t0) < 7:y() → 0. 155 y(fo) < 0: y() diverges from y=0.
Transcribed Image Text:y(to) - 7 for all y(to). /? /// / / Where a = 7. Equilibrium solutions: y(t) = 0 and y(f) = 7. %3D I IER 7/ E Behavior of y(t) as t → ∞ depends on initial value y(to): y(to) > 7: y(t) diverges from y = 7. 0 < y(to) < 7: y(t) → 7. y(to) < 0; y(1) diverges from y = 0. Where a = 7. Equilibrium solutions: y() = 0 and y(r) = 7. Behavior of y(t) as t → o depends on initial value y(to ): 555 y(to) > 7: y(1) diverges from y = 7. 0<y(t0) < 7:y() → 0. 155 y(fo) < 0: y() diverges from y=0.
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