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4. u" + wu = cos(wot)

4. u" + wu = cos(wot)

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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form for be Y(t) = (Aot + A₁) sint +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equat Problems 5220 In each of Problems 1 through 10, find the general solution of the given differential equation. Xy" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² 3. 4. 5. individually may For example, if g(t) = t sint+2 cost, the 6. y" + 2y' + y = 2e-t X. 8. Ⅱ. y"+y' - 6y = 12e³t+ 12e-2 ES GIBT y" - 2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) y"+y = 3 sin(2t) + t cos(2t) w² #wo b u" + wu = cos(wt), 152519 u" + wou = cos(wot) 10, y” +y+4y = 2 sinh t In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, y(0) = 0, y'(0) = 1 12. y" +4y=t² + 3e', y(0) = 0, y'(0) = 2 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 - Hint: sinh t = (e' — e-')/2 15. In each 2 u 201² M 0 16. y 17. J 18. y 19. y 20. y 21. y 22. C from E solution method nonhom where w
Transcribed Image Text:form for be Y(t) = (Aot + A₁) sint +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equat Problems 5220 In each of Problems 1 through 10, find the general solution of the given differential equation. Xy" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² 3. 4. 5. individually may For example, if g(t) = t sint+2 cost, the 6. y" + 2y' + y = 2e-t X. 8. Ⅱ. y"+y' - 6y = 12e³t+ 12e-2 ES GIBT y" - 2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) y"+y = 3 sin(2t) + t cos(2t) w² #wo b u" + wu = cos(wt), 152519 u" + wou = cos(wot) 10, y” +y+4y = 2 sinh t In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, y(0) = 0, y'(0) = 1 12. y" +4y=t² + 3e', y(0) = 0, y'(0) = 2 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 - Hint: sinh t = (e' — e-')/2 15. In each 2 u 201² M 0 16. y 17. J 18. y 19. y 20. y 21. y 22. C from E solution method nonhom where w
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