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18snil 1stno 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 → ∞. 1. 2. y' - 2y = 1²e²1 y'+3y=t+e-²¹ 3. y'+y=te +1 1 4. y' +y = 3 cos(21), 1>0 5. y' - 2y = 3e'

18snil 1stno 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 → ∞. 1. 2. y' - 2y = 1²e²1 y'+3y=t+e-²¹ 3. y'+y=te +1 1 4. y' +y = 3 cos(21), 1>0 5. y' - 2y = 3e'

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 7CR
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Problems 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. 1. 2. 3. 4. 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 y' - 2y = 1²e²21 y'+y=te +1 1 y' + y = 3 cos(2t), t> 0 y - 2y = 3e² ty' - y = 1²e, 1>0 y' + y = 5 sin(2t) 5. 6. 7. 8. 2y + y = 31² In each of Problems 9 through 12, find the solution of the given initial value problem. glovilnog werg 9. y' - y = 2te²¹, 10. y' + 2y = te-2t, 2 cost 11. y' + y = 7 y = 1² 9 12. ty' + (t+1)y=t, 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 ao be behavior depend on the choice of the initial value a? Let 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 ao exactly. 13. 14. 1 y' - Y 3y - 2y = e-T¹/2, y(0) = 1 2 cost, y(1) = 0 y() = 0, t> 0 y(ln 2) = 1, t > 0 c. Describe the behavior of the solution corresponding to the initial value ao. y(0) = a y(0) Aamia =
Transcribed Image Text:Problems 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. 1. 2. 3. 4. 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 y' - 2y = 1²e²21 y'+y=te +1 1 y' + y = 3 cos(2t), t> 0 y - 2y = 3e² ty' - y = 1²e, 1>0 y' + y = 5 sin(2t) 5. 6. 7. 8. 2y + y = 31² In each of Problems 9 through 12, find the solution of the given initial value problem. glovilnog werg 9. y' - y = 2te²¹, 10. y' + 2y = te-2t, 2 cost 11. y' + y = 7 y = 1² 9 12. ty' + (t+1)y=t, 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 ao be behavior depend on the choice of the initial value a? Let 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 ao exactly. 13. 14. 1 y' - Y 3y - 2y = e-T¹/2, y(0) = 1 2 cost, y(1) = 0 y() = 0, t> 0 y(ln 2) = 1, t > 0 c. Describe the behavior of the solution corresponding to the initial value ao. y(0) = a y(0) Aamia =
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