Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field, determine the behavior of y as t→ ∞0. If this behavior depends on the initial value of y at t = 0, describe this dependency. The equilibrium solution is y(t) = Solutions with initial values greater than 9 Choose one Solutions with initial values less than 9 Choose one

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 differential equation y'= (y - 9)².
Based on the direction field, determine the behavior of y as t→ ∞0.
If this behavior depends on the initial value of y at t = 0, describe
this dependency.
The equilibrium solution is
y(t)
=
Solutions with initial values greater than 9
Choose one
Solutions with initial values less than 9
Choose one
Transcribed Image Text:Draw a direction field for the differential equation y'= (y - 9)². Based on the direction field, determine the behavior of y as t→ ∞0. If this behavior depends on the initial value of y at t = 0, describe this dependency. The equilibrium solution is y(t) = Solutions with initial values greater than 9 Choose one Solutions with initial values less than 9 Choose one
Choose one
decrease toward the equilibrium solution.
diverge from the equilibrium solution.
increase toward the equilibrium solution.
Transcribed Image Text:Choose one decrease toward the equilibrium solution. diverge from the equilibrium solution. increase toward the equilibrium solution.
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