A.5.5: Section 5.5 Answers
- Page ID
- 43769
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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. \(y_{p}=\cos x+2\sin x\)
2. \(y_{p}=\cos x+(2-2x)\sin x\)
3. \(y_{p}=e^{x}(-2\cos x+3\sin x)\)
4. \(y_{p}=\frac{e^{2x}}{2}(\cos 2x-\sin 2x)\)
5. \(y_{p}=-e^{x}(x\cos x-\sin x)\)
6. \(y_{p} = e^{−2x} (1 − 2x)(\cos 3x − \sin 3x)\)
7. \(y_{p} = x(\cos 2x − 3 \sin 2x)\)
8. \(y_{p} = −x [(2 − x) \cos x + (3 − 2x) \sin x]\)
9. \(y_{p}=x\left[x\cos\left(\frac{x}{2}\right)-3\sin\left(\frac{x}{2}\right) \right]\)
10. \(y_{p} = xe^{−x} (3 \cos x + 4 \sin x)\)
11. \(y_{p} = xe^{x} [(−1 + x) \cos 2x + (1 + x) \sin 2x]\)
12. \(y_{p} = −(14 − 10x) \cos x − (2 + 8x − 4x^{2} ) \sin x\)
13. \(y_{p} = (1 + 2x + x^{2}) \cos x + (1 + 3x^{2}) \sin x\)
14. \(y_{p}=\frac{x^{2}}{2}(\cos 2x-\sin 2x)\)
15. \(y_{p} = e^{x} (x^{2} \cos x + 2 \sin x)\)
16. \(y_{p} = e^{x} (1 − x^{2} )(\cos x + \sin x)\)
17. \(y_{p} = e^{x} (x^{2} − x^{3})(\cos x + \sin x)\)
18. \(y_{p} = e^{−x} [(1 + 2x) \cos x − (1 − 3x) \sin x]\)
19. \(y_{p} = x(2 \cos 3x − \sin 3x)\)
20. \(y_{p} = −x^{3} \cos x + (x + 2x^{2} ) \sin x\)
21. \(y_{p} = −e^{−x}[ (x + x^{2} ) \cos x − (1 + 2x) \sin x]\)
22. \(y = e^{x} (2 \cos x + 3 \sin x) + 3e^{x} − e^{6x}\)
23. \(y = e^{x} [(1 + 2x) \cos x + (1 − 3x) \sin x]\)
24. \(y = e^{x} (\cos x−2 \sin x)+e^{−3x} (\cos x+\sin x)\)
25. \(y = e^{3x} [(2 + 2x) \cos x − (1 + 3x) \sin x]\)
26. \(y = e^{3x} [(2 + 3x) \cos x + (4 − x) \sin x]+3e^{x}−5e^{2x}\)
27. \(y_{p}=xe^{3x}-\frac{e^{x}}{5}(\cos x-2\sin x)\)
28. \(y_{p}=x(\cos x +2\sin x)-\frac{e^{x}}{2}(1-x)+\frac{e^{-x}}{2}\)
29. \(y_{p}=-\frac{xe^{x}}{2}(2+x)+2xe^{2x}+\frac{1}{10}(3\cos x+\sin x)\)
30. \(y_{p}=xe^{x}(\cos x+x\sin x)+\frac{e^{x}}{25}(4+5x)+1+x+\frac{x^{2}}{2}\)
31. \(y_{p}=\frac{x^{2}e^{2x}}{6}(3+x)-e^{2x}(\cos x-\sin x)+3e^{3x}+\frac{1}{4}(2+x)\)
32. \(y = (1 − 2x + 3x^{2})e^{2x} + 4 \cos x + 3 \sin x\)
33. \(y = xe^{−2x} \cos x + 3 \cos 2x\)
34. \(y=-\frac{3}{8}\cos 2x+\frac{1}{4}\sin 2x+e^{-x}-\frac{13}{8}e^{-2x}-\frac{3}{4}xe^{-2x}\)
40.
- \(2x \cos x − (2 − x^{2}) \sin x + c\)
- \(-\frac{e^{x}}{2}\left[ (1-x^{2})\cos x-(1-x)^{2}\sin x\right] +c\)
- \(-\frac{e^{-x}}{25}[(4+10x)\cos 2x-(3-5x)\sin 2x]+c\)
- \(-\frac{e^{-x}}{2}\left[ (1+x)^{2}\cos x-(1-x^{2})\sin x\right]+c\)
- \(-\frac{e^{x}}{2}\left[x(3-3x+x^{2})\cos x-(3-3x+x^{3})\sin x \right]+c\)
- \(-e^{x}[(1-2x)\cos x+(1+x)\sin x]+c\)
- \(e^{-x}[x\cos x+x(1+x)\sin x]+c\)