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Mathematics LibreTexts

Section 9.3 Answers

  • Page ID
    29617
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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. \(2+e^{x}\left[ (1+x)\cos x-\sin x-1\right]\)