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Buff 2.5 Problems In Problems I through 20, find a particular solution y, of the given equation. In all these problems, primes denote deriva- tives with respect to x. y" + 16y=el -6y=2 sin 3x H4 5. y"+y+y = sin² x 6. 2 y"-y-2y = 3x +4 4y" +4y+y = 3xe' 2y" +4y' + 7y=x² (b) Use the re Use trigonometr equations in Pro

Buff 2.5 Problems In Problems I through 20, find a particular solution y, of the given equation. In all these problems, primes denote deriva- tives with respect to x. y" + 16y=el -6y=2 sin 3x H4 5. y"+y+y = sin² x 6. 2 y"-y-2y = 3x +4 4y" +4y+y = 3xe' 2y" +4y' + 7y=x² (b) Use the re Use trigonometr equations in Pro

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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mple given (33) and mply s in 2.5 Problems In Problems I through 20, find a particular solution y, of the given equation. In all these problems, primes denote deriva- tives with respect to x. y" + 16y=e³x 3y"-y-6y=2 sin 3x H 5. y + y + y = sin² x hyo yo sinh x 9. y + 2y - 3y = 1+xe* +9y2 cos 3x + 3 sin 3x + 4y = 3x - 1 13. y +2y + 5y = e' sin x 15. y) +Sy(4) - y = 17 10. y 11. y HM 17. y + y = sin x + x cos x 18, 5g nghi lycxe 19. y) +2y3) + 2y" = 3x² - 1 20. y-y=e² +7 2.5 Nonhomogeneous Equations and Undeter 6. 8. y" - y' - 2y = 3x + 4 4y" + 4y + y = 3xe* 2y" +4y' + 7y=x² y - 4y = cosh 2x 12. y(3) + y'= 2-sinx 14.7 y(4) - 2y" + y = xe² 16 y" +9y = 2x²e³x +5 In Problems 21 through 30, set up the appropriate form of a particular solution y,, but do not determine the values of the coefficients 21.-2y + 2y = e sinx 22. y - y) = ² + 2x² - 5 23. y + 4y= 3x cos 2x 24. y-y-12y = x-2xe-x 25.+3y + 2y = x(e^²-e-²) 26. -6y + 13y = xe" sin 2x 27. y + 5y + 4y= sinx + cos2x 28. +9y" = (x²+1) sin 3x 29. (D-1) (D2-4)y=xe²+²+e-2 30. -2y+y=x² cosx Solve the initial value problems in Problems 31 through 40. (b) Use the result of pa Use trigonometric identiti equations in Problems 44 44. y" + y + y = sinxs 45. y" +9y= sinº x 46. y + y = x cos³ x In Problems 47 through rameters to find a parti equation. 47. y" + 3y + 2y = 4 49. y" - 4y + 4y = 2 51. y" +4y= cos 3x 53. y" +9y=2 sec 3 55. y + 4y= sin x 57. You can verify b complementary order equation But before ap ters, you must efficient x² to
Transcribed Image Text:mple given (33) and mply s in 2.5 Problems In Problems I through 20, find a particular solution y, of the given equation. In all these problems, primes denote deriva- tives with respect to x. y" + 16y=e³x 3y"-y-6y=2 sin 3x H 5. y + y + y = sin² x hyo yo sinh x 9. y + 2y - 3y = 1+xe* +9y2 cos 3x + 3 sin 3x + 4y = 3x - 1 13. y +2y + 5y = e' sin x 15. y) +Sy(4) - y = 17 10. y 11. y HM 17. y + y = sin x + x cos x 18, 5g nghi lycxe 19. y) +2y3) + 2y" = 3x² - 1 20. y-y=e² +7 2.5 Nonhomogeneous Equations and Undeter 6. 8. y" - y' - 2y = 3x + 4 4y" + 4y + y = 3xe* 2y" +4y' + 7y=x² y - 4y = cosh 2x 12. y(3) + y'= 2-sinx 14.7 y(4) - 2y" + y = xe² 16 y" +9y = 2x²e³x +5 In Problems 21 through 30, set up the appropriate form of a particular solution y,, but do not determine the values of the coefficients 21.-2y + 2y = e sinx 22. y - y) = ² + 2x² - 5 23. y + 4y= 3x cos 2x 24. y-y-12y = x-2xe-x 25.+3y + 2y = x(e^²-e-²) 26. -6y + 13y = xe" sin 2x 27. y + 5y + 4y= sinx + cos2x 28. +9y" = (x²+1) sin 3x 29. (D-1) (D2-4)y=xe²+²+e-2 30. -2y+y=x² cosx Solve the initial value problems in Problems 31 through 40. (b) Use the result of pa Use trigonometric identiti equations in Problems 44 44. y" + y + y = sinxs 45. y" +9y= sinº x 46. y + y = x cos³ x In Problems 47 through rameters to find a parti equation. 47. y" + 3y + 2y = 4 49. y" - 4y + 4y = 2 51. y" +4y= cos 3x 53. y" +9y=2 sec 3 55. y + 4y= sin x 57. You can verify b complementary order equation But before ap ters, you must efficient x² to
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