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Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. y" differential equation. In each c Xy"-2y' - 3y = 3e21 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. y" +2y + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(21) 8. u"+wu = cos(wt), w²w² S. 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. 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² + 3e', y(0) = 0, y(0) = 0, y(0) = y'(0) = 1 y'(0) = 2 13. y" - 2y + y = te' +4, 1, y'(0) = 1 14. y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 unc N of 16. y 17. y 18. y 19. y 20. y 21. y 22. C from E solution method nonhor where

Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. y" differential equation. In each c Xy"-2y' - 3y = 3e21 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. y" +2y + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(21) 8. u"+wu = cos(wt), w²w² S. 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. 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² + 3e', y(0) = 0, y(0) = 0, y(0) = y'(0) = 1 y'(0) = 2 13. y" - 2y + y = te' +4, 1, y'(0) = 1 14. y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 unc N of 16. y 17. y 18. y 19. y 20. y 21. y 22. C from E solution method nonhor where

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 equation. Problems 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. 6. y" + 2y' + y = 2e¹ 7. y"+y' - 6y = 12e³t + 12e -2t y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) y" + y = 3 sin(2t) + t cos(2t) 2 2 8. u" + wu = cos(wt), w² #wo 9. u" + wu = cos(wot) 10. y” +y+4y=2 sinht In each of Problems 11 through 15, find the solution of the given initial value problem. 11. 12. - Hint: sinht = (e – e )/2 y"+y'-2y = 2t, y(0) = 0, y'(0) = 1 y" + 4y = 1² +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 15. y" In each c unc N of t 16. y" 17. y 18. y' 19. y 20. y 21. y' 22. C from E solution method nonhor where
Transcribed Image Text:Y(t) = (Aot + A₁) sint +(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems 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. 6. y" + 2y' + y = 2e¹ 7. y"+y' - 6y = 12e³t + 12e -2t y" - 2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) y" + y = 3 sin(2t) + t cos(2t) 2 2 8. u" + wu = cos(wt), w² #wo 9. u" + wu = cos(wot) 10. y” +y+4y=2 sinht In each of Problems 11 through 15, find the solution of the given initial value problem. 11. 12. - Hint: sinht = (e – e )/2 y"+y'-2y = 2t, y(0) = 0, y'(0) = 1 y" + 4y = 1² +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 15. y" In each c unc N of t 16. y" 17. y 18. y' 19. y 20. y 21. y' 22. C from E solution method nonhor where
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