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
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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