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differential equation of the form y' (t) = F(y) is said to be autonomous (the function F depends only on y). The constant function y = yo is an equilibrium solution of the equation provided F (Yo) =0 (because then y'(t) = 0, and the solution remains onstant for all t). Note that equilibrium solutions correspond - (c) below. o horizontal line segments in the direction field. Note also that for autonomous equations, the direction field is independent of t. Consider the equation y'(t) = y(y + 6). Complete parts (a) a) Find all equilibrium solutions. = (Simplify your answer. Use a comma to separate answers as needed.) ) Sketch the direction field on either side of the equilibrium solution(s) for t20. Choose the correct answer below. DA. OB. Oc. y -1 :) Sketch the solution curve that corresponds to the initial condition y(0) = - 1. Choose the correct answer below. DA. В. OC.

differential equation of the form y' (t) = F(y) is said to be autonomous (the function F depends only on y). The constant function y = yo is an equilibrium solution of the equation provided F (Yo) =0 (because then y'(t) = 0, and the solution remains onstant for all t). Note that equilibrium solutions correspond - (c) below. o horizontal line segments in the direction field. Note also that for autonomous equations, the direction field is independent of t. Consider the equation y'(t) = y(y + 6). Complete parts (a) a) Find all equilibrium solutions. = (Simplify your answer. Use a comma to separate answers as needed.) ) Sketch the direction field on either side of the equilibrium solution(s) for t20. Choose the correct answer below. DA. OB. Oc. y -1 :) Sketch the solution curve that corresponds to the initial condition y(0) = - 1. Choose the correct answer below. DA. В. OC.

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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A differential equation of the form y'(t) = F(y) is said to be autonomous (the function F depends only on y). The constant function y = yo is an equilibrium solution of the equation provided F (yo) = 0 (because then y'(t) = 0, and the solution remains constant for all t). Note that equilibrium solutions correspond to horizontal line segments in the direction field. Note also that for autonomous equations, the direction field is independent of t. Consider the equation y'(t) = y(y + 6). Complete parts (a) to (c) below. (a) Find all equilibrium solutions. y = (Simplify your answer. Use a comma to separate answers as needed.) (b) Sketch the direction field on either side of the equilibrium solution(s) for t>0. Choose the correct answer below. OA. В. Ос. y y y (c) Sketch the solution curve that corresponds to the initial condition y(0) = - 1. Choose the correct answer below. O A. В. С. y y y -1
Transcribed Image Text:A differential equation of the form y'(t) = F(y) is said to be autonomous (the function F depends only on y). The constant function y = yo is an equilibrium solution of the equation provided F (yo) = 0 (because then y'(t) = 0, and the solution remains constant for all t). Note that equilibrium solutions correspond to horizontal line segments in the direction field. Note also that for autonomous equations, the direction field is independent of t. Consider the equation y'(t) = y(y + 6). Complete parts (a) to (c) below. (a) Find all equilibrium solutions. y = (Simplify your answer. Use a comma to separate answers as needed.) (b) Sketch the direction field on either side of the equilibrium solution(s) for t>0. Choose the correct answer below. OA. В. Ос. y y y (c) Sketch the solution curve that corresponds to the initial condition y(0) = - 1. Choose the correct answer below. O A. В. С. y y y -1
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