# 11.59: A.9.3 Section 9.3 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. $$2+e^{x}\left[ (1+x)\cos x-\sin x-1\right]$$

This page titled 11.59: A.9.3 Section 9.3 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.