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7. y"+y = 3 sin(2t) + t cos(2t)

7. y"+y = 3 sin(2t) + t cos(2t)

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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Y(t) = (Aot + A₁) sint +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous eq Problems In each of Problems 1 through 10, find the general solution of the given differential equation. y" - 2y' - 3y = 3e²r y" - y' - 2y = -2t+4t² y"+y' - 6y = 12e³+ 12e-2 y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 1 X. 2. 3. 4. 5. 6. y" +2y' + y = 2e-¹ 7. y" + y = 3 sin(2t) + t cos(21) 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"+y' - 2y = 2t, 11. 12. y" + 4y = 1² + 3e', 13. y" - 2y + y = te' +4, 14. y(0) = 1, y'(0) = 1 y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 1 In 1 1 1 1 2 2 2 fr SC m no W
Transcribed Image Text:Y(t) = (Aot + A₁) sint +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous eq Problems In each of Problems 1 through 10, find the general solution of the given differential equation. y" - 2y' - 3y = 3e²r y" - y' - 2y = -2t+4t² y"+y' - 6y = 12e³+ 12e-2 y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 1 X. 2. 3. 4. 5. 6. y" +2y' + y = 2e-¹ 7. y" + y = 3 sin(2t) + t cos(21) 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"+y' - 2y = 2t, 11. 12. y" + 4y = 1² + 3e', 13. y" - 2y + y = te' +4, 14. y(0) = 1, y'(0) = 1 y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 1 In 1 1 1 1 2 2 2 fr SC m no W
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