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14.45: Section 9.3 Answers

Last updated

Aug 11, 2020
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- 14.44: Section 9.2 Answers
- 14.46: Section 9.4 Answers

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1. $y_{p}=e^{-x}(2+x-x^{2})$

2. $y_{p}=-\frac{e^{-3x}}{4}(3-x+x^{2})$

3. $y_{p}=e^{x}(1+x-x^{2})$

4. $y_{p}=e^{-2x}(1-5x+x^{2})$

5. $y_{p}=-\frac{xe^{x}}{2}(1-x+x^{2}-x^{3})$

6. $y_{p}=x^{2}e^{x}(1+x)$

7. $y_{p}=\frac{xe^{-2x}}{2}(2+x)$

8. $y_{p}=\frac{x^{2}e^{x}}{2}(2+x)$

9. $y_{p}=\frac{x^{2}e^{2x}}{2}(1+2x)$

10. $y_{p}=x^{2}e^{3x}(2+x-x^{2})$

11. $y_{p}=x^{2}e^{4x}(2+x)$

12. $y_{p}=\frac{x^{3}e^{x/2}}{48}(1+x)$

13. $y_{p}=e^{-x}(1-2x+x^{2})$

14. $y_{p}=e^{2x}(1-x)$

15. $y_{p}=e^{-2x}(1+x+x^{2}-x^{3})$

16. $y_{p}=\frac{e^{x}}{3}(1-x)$

17. $y_{p}=e^{x}(1+x)^{2}$

18. $y_{p}=xe^{x}(1+x^{3})$

19. $y_{p}=xe^{x}(2+x)$

20. $y_{p}=\frac{xe^{2x}}{6}(1-x^{2})$

21. $y_{p}=4xe^{-x/2}(1+x)$

22. $y_{p}=\frac{xe^{x}}{6}(1+x^{2})$

23. $y_{p}=\frac{x^{2}e^{2x}}{6}(1+x+x^{2})$

24. $y_{p}=\frac{x^{2}e^{2x}}{6}(3+x+x^{2})$

25. $y_{p}=\frac{x^{3}e^{x}}{48}(2+x)$

26. $y_{p}=\frac{x^{3}e^{x}}{6}(1+x)$

27. $y_{p}=-\frac{x^{3}e^{-x}}{6}(1-x+x^{2})$

28. $y_{p}=\frac{x^{3}e^{2x}}{12}(2+x-x^{2})$

29. $y_{p} = e^{−x} \left[ (1 + x) \cos x + (2 − x) \sin x\right]$

30. $y_{p}=e^{-x}\left[ (1-x)\cos 2x+(1+x)\sin 2x\right]$

31. $y_{p}=e^{2x}\left[ (1+x-x^{2})\cos x +(1+2x)\sin x\right]$

32. $y_{p}=\frac{e^{x}}{2}\left[ (1+x)\cos 2x+(1-x+x^{2})\sin 2x\right]$

33. $y_{p}=\frac{x}{13}(8\cos 2x+14\sin 2x)$

34. $y_{p}=xe^{x}\left[ (1+x)\cos x+(3+x)\sin x\right]$

35. $y_{p}=\frac{xe^{2x}}{2}\left[(3-x)\cos 2x+\sin 2x\right]$

36. $y_{p}=-\frac{xe^{3x}}{12}(x\cos 3x+\sin 3x)$

37. $y_{p}=-\frac{e^{x}}{10}(\cos x+7\sin x)$

38. $y_{p}=\frac{e^{x}}{12}(\cos 2x-\sin 2x)$

39. $y_{p}=xe^{2x}\cos 2x$

40. $y_{p}=-\frac{e^{-x}}{2}\left[ (1+x)\cos x+(2-x)\sin x\right]$

41. $y_{p}=\frac{xe^{-x}}{10}(\cos x+2\sin x)$

42. $y_{p}=\frac{xe^{x}}{4-}(3\cos 2x-\sin 2x)$

43. $y_{p}=\frac{xe^{-2x}}{8}\left[(1-x)\cos 3x+(1+x)\sin 3x\right]$

44. $y_{p}=-\frac{xe^{x}}{4}(1+x)\sin 2x$

45. $y_{p}=\frac{x^{2}e^{-x}}{4}(\cos x-2\sin x)$

46. $y_{p}=-\frac{x^{2}e^{2x}}{32}(\cos 2x-\sin 2x)$

47. $y_{p}=\frac{x^{2}e^{2x}}{8}(1+x)\sin x$

48. $y_{p}=2x^{2}e^{x}+xe^{2x}-\cos x$

49. $y_{p}=e^{2x}+xe^{x}+2x\cos x$

50. $y_{p}=2x+x^{2}+2xe^{x}-3xe^{-x}+4e^{3x}$

51. $y_{p}=xe^{x}(\cos 2x-2\sin 2x)+2xe^{2x}+1$

52. $y_{p}=x^{2}e^{-2x}(1+2x)-\cos 2x+\sin 2x$

53. $y_{p}=2x^{2}(1+x)e^{-x}+x\cos x-2\sin x$

54. $y_{p}=2xe^{x}+xe^{2x}+\cos x$

55. $y_{p}=\frac{xe^{x}}{6}(\cos x+\sin 2x)$

56. $y_{p}=\frac{x^{2}}{54}\left[(2+2x)e^{x}+3e^{-2x}\right]$

57. $y_{p}=\frac{x}{8}\sinh x\sin x$

58. $y_{p}=x^{3}(1+x)e^{-x}+xe^{-2x}$

59. $y_{p}=xe^{x}(2x^{2}+\cos x+\sin x)$

60. $y=e^{2x}(1+x)+c_{1}e^{-x}+e^{x}(c_{2}+c_{3}x)$

61. $y=e^{3x}\left( 1-x-\frac{x^{2}}{2}\right)+c_{1}e^{x}+e^{-x}(c_{2}\cos x+c_{3}\sin x)$

62. $y=xe^{2x}(1+x)^{2}+c_{1}e^{x}+c_{2}e^{2x}+c_{3}e^{3x}$

63. $y=x^{2}e^{-x}(1-x)^{2}+c_{1}+e^{-x}(c_{2}+c_{3}x)$

64. $y=\frac{x^{3}e^{x}}{24}(4+x)+e^{x}(c_{1}+c_{2}x+c_{3}x^{2})$

65. $y=\frac{x^{2}e^{-x}}{16}(1+2x-x^{2})+e^{x}(c_{1}+c_{2}x)+e^{-x}(c_{3}+c_{4}x)$

66. $y=e^{-2x}\left[\left(1+\frac{x}{2}\right)\cos x+\left(\frac{3}{2}-2x\right)\sin x\right] +c_{1}e^{x}+c_{2}e^{-x}+c_{3}e^{-2x}$

67. $y=-xe^{x}\sin 2x+c_{1}+c_{2}e^{x}+e^{x}(c_{3}\cos x+c_{4}\sin x)$

68. $y=-\frac{x^{2}e^{x}}{16}(1+x)\cos 2x+e^{x}\left[ (c_{1}+c_{2}x)\cos 2x+(c_{3}+c_{4}x)\sin 2x\right]$

69. $y=(x^{2}+2)e^{x}-e^{-2x}+e^{3x}$

70. $y=e^{-x}(1+x+x^{2})+(1-x)e^{x}$

71. $y=\left(\frac{x^{2}}{12}+16\right)xe^{-x/2}-e^{x}$

72. $y=(2-x)(x^{2}+1)e^{-x}+\cos x-\sin x$

73. $y=(2-x)\cos x-(1-7x)\sin x+e^{-2x}$

74. $2+e^{x}\left[ (1+x)\cos x-\sin x-1\right]$

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