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9. u" + wu = cos(wot) 2

9. u" + wu = cos(wot) 2

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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Question

9 pl

(Bot + B₁) cos i provided that sint and cost are not solutions of the homogeneous e Problems In each of Problems 1 through 10, find the general solution of the given differential equation. Xy"-2y' - 3y = 3e²1 2. y" - y' - 2y = -2t+4t² 3. 4. do di y"+y' - 6y = 12e³t + 12e-2t y" - 2y' - 3y = -3te-¹ 5. y" + 2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ 7. y"+y = 3 sin(21) + t cos(2t) 8. u" + wu = cos(wt), w² #wo 9. u" + wou = 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) = 0, y'(0) = 1 y(0) = 0, y'(0) = 2 y(0) = 1, y'(0) = 1 y(0) = 2, y'(0) = -1 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² +3e', 13. y" - 2y + y = te' +4, 14. y" + 4y = 3 sin(2t), 15 In 16. 17. 18. 19. 20. 21. 22. from soluti metho nonho where
Transcribed Image Text:(Bot + B₁) cos i provided that sint and cost are not solutions of the homogeneous e Problems In each of Problems 1 through 10, find the general solution of the given differential equation. Xy"-2y' - 3y = 3e²1 2. y" - y' - 2y = -2t+4t² 3. 4. do di y"+y' - 6y = 12e³t + 12e-2t y" - 2y' - 3y = -3te-¹ 5. y" + 2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ 7. y"+y = 3 sin(21) + t cos(2t) 8. u" + wu = cos(wt), w² #wo 9. u" + wou = 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) = 0, y'(0) = 1 y(0) = 0, y'(0) = 2 y(0) = 1, y'(0) = 1 y(0) = 2, y'(0) = -1 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² +3e', 13. y" - 2y + y = te' +4, 14. y" + 4y = 3 sin(2t), 15 In 16. 17. 18. 19. 20. 21. 22. from soluti metho nonho where
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