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y" - 2y' - 3y = 3e²t

y" - 2y' - 3y = 3e²t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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COS I, provided that sint and cost are not solutions of the homogeneous equatio Problems In each of Problems 1 through 10, find the general solution of the given differential equation. 1. y"-2y' - 3y = 3e2¹ 2. y" - y' - 2y = -2t+41² 3. y"+y' - 6y = 12e3+ 12e7 -2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. 7. y" + 2y' + y = 2e¹ y" + y = 3 sin(21) + t cos(2t) 8. u" + wu = cos(wt), w² #wo 9. u" + w₁u = cos(wot) 10. y” + y+4y = 2 sinh t - Hint: sinht =(e' – e^')/2 In each of Problems 11 through 15, find the solution of the given initial value problem. y'(0) = 1 y'(0) = 2 13. y" - 2y' + y = te' +4, y(0) = 1, y'(0) = 1 14. y" + 4y = 3 sin(2r), y(0) = 2, y'(0) = -1 y"+y'-2y = 2t, 11. 12. y" + 4y = 1² +3e', y(0) = 0, y(0) = 0, 15. : In eac A L 16. 17. 18. 19. 20. : 21. : 22. C from E solutio method nonhor where
Transcribed Image Text:COS I, provided that sint and cost are not solutions of the homogeneous equatio Problems In each of Problems 1 through 10, find the general solution of the given differential equation. 1. y"-2y' - 3y = 3e2¹ 2. y" - y' - 2y = -2t+41² 3. y"+y' - 6y = 12e3+ 12e7 -2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. 7. y" + 2y' + y = 2e¹ y" + y = 3 sin(21) + t cos(2t) 8. u" + wu = cos(wt), w² #wo 9. u" + w₁u = cos(wot) 10. y” + y+4y = 2 sinh t - Hint: sinht =(e' – e^')/2 In each of Problems 11 through 15, find the solution of the given initial value problem. y'(0) = 1 y'(0) = 2 13. y" - 2y' + y = te' +4, y(0) = 1, y'(0) = 1 14. y" + 4y = 3 sin(2r), y(0) = 2, y'(0) = -1 y"+y'-2y = 2t, 11. 12. y" + 4y = 1² +3e', y(0) = 0, y(0) = 0, 15. : In eac A L 16. 17. 18. 19. 20. : 21. : 22. C from E solutio method nonhor where
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