A.9.3 Section 9.3 Answers
- Page ID
- 43792
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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. \(2+e^{x}\left[ (1+x)\cos x-\sin x-1\right]\)