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mation 9. y'-y = 2te²¹, y(0) = 1 2

mation 9. y'-y = 2te²¹, y(0) = 1 2

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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In each of Problems 1 through 8: Ga. Draw a direction field for the given differential equation. b. Based on an inspection of the direction field, describe how solutions behave for large t. c. Find the general solution of the given differential equation, and use it to determine how solutions behave as t → ∞. y'+3y=t+e=²1 1. 2. y' - 2y = 1²e²t 3. y' + y = te¯¹ +1 4. y' + −y=3 cos(21), t> 0 5. y' - 2y = 3e¹ 6. ty' - y = t²e¯¹, t>0 7. y' + y = 5 sin(2t) 8. 2y' + y = 3t² In each of Problems 9 through 12, find the solution of the given initial value problem. 9. y' - y = 2te²¹, 10. y' +2y=te-²¹, y(0)=1 2 Cost 11. y' + − y = ¯7²3 p. y(π) = 0, t> 0 12. ty'+(t+1)y=t, y(ln2) = 1, t > 0 In each of Problems 13 and 14: Ga. Draw a direction field for the given differential equation. How do solutions appear to behave as t becomes large? Does the behavior depend on the choice of the initial value a? Let að be the value of a for which the transition from one type of behavior to another occurs. Estimate the value of ao. b. Solve the initial value problem and find the critical value do exactly. 13. y(1) = 0 1 y y = 2 cost, う 14. 3y - 2y = e-πt/2₂ c. Describe the behavior of the solution corresponding to the initial value ao. y(0) = = a y(0) = a
Transcribed Image Text:In each of Problems 1 through 8: Ga. Draw a direction field for the given differential equation. b. Based on an inspection of the direction field, describe how solutions behave for large t. c. Find the general solution of the given differential equation, and use it to determine how solutions behave as t → ∞. y'+3y=t+e=²1 1. 2. y' - 2y = 1²e²t 3. y' + y = te¯¹ +1 4. y' + −y=3 cos(21), t> 0 5. y' - 2y = 3e¹ 6. ty' - y = t²e¯¹, t>0 7. y' + y = 5 sin(2t) 8. 2y' + y = 3t² In each of Problems 9 through 12, find the solution of the given initial value problem. 9. y' - y = 2te²¹, 10. y' +2y=te-²¹, y(0)=1 2 Cost 11. y' + − y = ¯7²3 p. y(π) = 0, t> 0 12. ty'+(t+1)y=t, y(ln2) = 1, t > 0 In each of Problems 13 and 14: Ga. Draw a direction field for the given differential equation. How do solutions appear to behave as t becomes large? Does the behavior depend on the choice of the initial value a? Let að be the value of a for which the transition from one type of behavior to another occurs. Estimate the value of ao. b. Solve the initial value problem and find the critical value do exactly. 13. y(1) = 0 1 y y = 2 cost, う 14. 3y - 2y = e-πt/2₂ c. Describe the behavior of the solution corresponding to the initial value ao. y(0) = = a y(0) = a
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