33: Section 9.3 Answers
- Page ID
- 103653
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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. \(y=-1+e^t\)
2. \(y=-3e^{-t/2}\)
3. \(y={1\over 10}e^{4t}+{19\over 10}e^{-6t}\)
4. \(y={1\over 13}e^{t}-{1\over 13}\cos 5t+{5\over 13}\sin 5t\)
5. \(y={4\over 3}e^{-t}-{1\over 3}e^{-4t}\)
6. \(y={5\over 2}-2e^{3t}-{3\over 5}e^{-t}+{11\over 10}e^{4t}\)
7. \(y=10\cos t+2\sin t-\sqrt2\sin\sqrt2 t\)
8. \(y={1\over 10}e^{t}-{1\over 30}\sin 3t-{1\over 10}\cos 3t\)
9. \(y={1\over 2}e^{-t}+{5\over 18}e^t-{8\over 9}e^{-t/2}+{1\over 9}e^{-2t}\)
10. \(y={13\over 60}e^{t}-{13\over 20}e^{-t}+{16\over 39}e^{-2t}+{3\over 130}\cos 3t-{1\over 65}\sin 3t\)
11. \(y=\frac{1}{6}e^{t}-\frac{9}{2}e^{-t}+\frac{16}{3}e^{-2t}\)
12. \(y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}\)
13. \(y=-\frac{23}{15}e^{-2t}+\frac{1}{3}e^{t}+\frac{1}{5}e^{3t}\)
14. \(y=-\frac{1}{4}e^{2t}+\frac{17}{20}e^{-2t}+\frac{2}{5}e^{3t}\)
15. \(y=\frac{11}{15}e^{-2t}+\frac{1}{6}e^{t}+\frac{1}{10}e^{3t}\)
16. \(y=e^{t}+2e^{-2t}-2e^{-t}\)
17. \(y=\frac{5}{3}\sin t-\frac{1}{3}\sin 2t\)
18. \(y=4e^{t}-4e^{2t}+e^{3t}\)
19. \(y=-\frac{7}{2}e^{2t}+\frac{13}{3}e^{t}+\frac{1}{6}e^{4t}\)
20. \(y=\frac{5}{2}e^{t}-4e^{2t}+\frac{1}{2}e^{3t}\)
21. \(y=\frac{1}{3}e^{t}-2e^{-t}+\frac{5}{3}e^{-2t}\)
22. \(y=2-e^{-2t}+e^{t}\)
23. \(y=1-\cos 2t+\frac{1}{2}\sin 2t\)
24. \(y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}\)
25. \(y=\frac{1}{6}e^{t}-\frac{2}{3}e^{-2t}+\frac{1}{2}e^{-t}\)
26. \(y=-1+e^{t}+e^{-t}\)
27. \(y=\cos 2t-\sin 2t+\sin t\)
28. \(y=\frac{7}{3}-\frac{7}{2}e^{-t}+\frac{1}{6}e^{3t}\)
29. \(y=1+\cos t\)
30. \(y=t+\sin t\)
31. \(y=t-6\sin t+\cos t+\sin 2t\)
32. \(y=e^{-t}+4e^{-2t}-4e^{-3t}\)
33. \(y=-\sin t-2\cos t+3e^{3t}+e^{-t}\)
34. \(y=\frac{1}{5}e^{2t}-\frac{4}{3}e^{t}+\frac{32}{15}e^{-t/2}\)
35. \(y=\frac{1}{7}e^{2t}-\frac{2}{5}e^{t/2}+\frac{9}{35}e^{-t/3}\)