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13. y" - 2y' + y = te' +4, y(0) = 1, y'(0) = 1

13. y" - 2y' + y = te' +4, y(0) = 1, y'(0) = 1

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

13 pl

provided that sint and cost are not solutions of the homogeneous equat Problems In each of Problems 1 through 10, find the general solution of the given differential equation. 1. y" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(2t) 2 8. u" + wu = cos(wt), w² #w² № be 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. 11. y"+y'-2y = 2t, 12. y" +4y= 1² + 3e', 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 y(0) = 0, y(0) = 0, y'(0) = 1 y'(0) = 2 15. In e 16 17 18 19 20 2 2 fi S m r I
Transcribed Image Text:provided that sint and cost are not solutions of the homogeneous equat Problems In each of Problems 1 through 10, find the general solution of the given differential equation. 1. y" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(2t) 2 8. u" + wu = cos(wt), w² #w² № be 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. 11. y"+y'-2y = 2t, 12. y" +4y= 1² + 3e', 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 y(0) = 0, y(0) = 0, y'(0) = 1 y'(0) = 2 15. In e 16 17 18 19 20 2 2 fi S m r I
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