34: Section 9.4 Answers
- Page ID
- 103654
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. \({1\over (s-10)^2}\)
2. \({6\over (s+2)^4}\)
3. \({3\over (s-1)^2+9}\)
4. \({1\over s-6}+{3\over (s-6)^2}-{2\over (s-6)^3}\)
5. \({s\over s^2-16}+{s-1\over (s-1)^2-16}-3{s+2\over (s+2)^2-16}\)
6. \(\frac{t^{3}e^{7t}}{2}\)
7. \(2e^{2t}\cos 3t\)
8. \(\frac{e^{-2t}}{4}\sin 4t\)
9. \(\frac{e^{2t}}{2}\sinh 2t\)
10. \(\frac{2e^{3t}}{3}\sinh 3t\)
11. \(t^{2}e^{7t}+\frac{17}{6}t^{3}e^{7t}\)
12. \(e^{2t}\left(\frac{1}{6}t^{3}+\frac{1}{6}t^{4}+\frac{1}{40}t^{5}\right)\)
13. \(e^{-3t}\left(\cos 3t+\frac{2}{3}\sin 3t\right)\)
14. \((1-t)e^{-t}\)
15. \(\left( 1-t-t^{2}-\frac{1}{6}t^{3}\right)e^{-t}\)
16. \(e^{t}\left(2\cos 2t+\frac{5}{2}\sin 2t\right)\)
17. \(3te^{-2t}-2\cos 2t-3\sin 2t\)
18. \(\frac{2}{5}\sin t+\frac{6}{5}\cos t+\frac{7}{5}e^{-t}\sin t-\frac{6}{5}e^{-t}\cos t\)
19. \(\frac{8}{13}e^{2t}-\frac{8}{13}e^{-t}\cos 2t+\frac{15}{26}e^{-t}\sin 2t\)
20. \(e^{t}(\cos 2t+\sin 2t)-e^{-t}\left( \cos 3t+\frac{4}{3}\sin 3t\right)\)
21. \(e^{3t}\left(-\cos 2t+\frac{3}{2}\sin 2t\right)+e^{-t}\left(\cos 2t+\frac{1}{2}\sin 2t\right)\)
22. \(e^{-2t}\left(\frac{1}{8}\cos t+\frac{1}{4}\sin t\right)-e^{2t}\left(\frac{1}{8}\cos 3t-\frac{1}{12}\sin 3t\right)\)
23. \(e^{2t}\left(\cos t+\frac{1}{2}\sin t\right)-e^{3t}\left(\cos 2t-\frac{1}{4}\sin 2t\right)\)
24 \(e^{t}\left(\frac{1}{5}\cos t+\frac{2}{5}\sin t\right)-e^{-t}\left(\frac{1}{5}\cos 2t+\frac{2}{5}\sin 2t\right)\)
25. \(e^{t/2}\left(-\cos t+\frac{9}{8}\sin t\right)+e^{-t/2}\left(\cos t-\frac{1}{8}\sin t\right)\)
26. \(\frac{e^{t}}{16}(1-\cos 4t)\)
27. \(\frac{4}{9}e^{2t}+\frac{5}{9}e^{-t}\sin 3t-\frac{4}{9}e^{-t}\cos 3t\)
28. \(3e^{t/2}-\frac{7}{2}e^{t}\sin 2t-3e^{t}\cos 2t\)
29. \(\frac{1}{4}e^{3t}-\frac{1}{4}e^{-t}\cos 2t\)
30. \(\frac{1}{9}e^{2t}-\frac{1}{9}e^{-t}\cos 3t+\frac{5}{9}e^{-t}\sin 3t\)
31. \(-\frac{3}{5}e^{-t}\sin t+\frac{1}{5}e^{-t}\cos t-\frac{1}{2}e^{-t}+\frac{3}{10}e^{t}\)
32. \(-\frac{1}{10}e^{t}\sin t-\frac{7}{10}e^{t}\cos t+\frac{1}{5}e^{-t}+\frac{1}{2}e^{2t}\)
33. \(\frac{3}{10}+\frac{1}{10}e^{2t}+\frac{1}{10}e^{t}\sin 2t-\frac{2}{5}e^{t}\cos 2t\)
34. \(-\frac{4}{9}e^{2t}\cos 3t+\frac{1}{3}e^{2t}\sin 3t-\frac{5}{9}e^{2t}+e^{t}\)
35. \(y=te^{-4t}+2e^{-4t}\)
36. \(y=e^{-t}+2te^{-t}\)
37. \(y={1\over 9}t+{2\over 27}-{2\over 27}e^{3t}+{10\over 9}te^{3t}\)
38. \(y=-{3\over 2}e^{3t}\sin 2t\)
39. \({1\over 2}-{1\over 2}e^t\cos t+{1\over 2}e^t\sin t\)
40. \(y=-3\cos t-2\sin t+e^{-t}(2+5t)\)
41. \(y=e^{t}(\cos t-3\sin t)+e^{3t}\)
42. \(y=-1+t+e^{-t}(3\cos t-5\sin t)\)
43. \(y=4\cos t-3\sin t-e^{t}(3\cos t-8\sin t)\)
44. \(y=e^{-t}-2e^{t}+e^{-2t}(\cos 3t- 11/3\sin 3t)\)
45. \(y=e^{-t}(\sin t-\cos t)+e^{-2t}(\cos t+4\sin t)\)
46. \(y=e^{-t/2}(5\cos (t/2)-\sin (t/2))+2t-4\)
47. \(y=\frac{1}{17}(12\cos t+20\sin t-3e^{t/2}(4\cos t+\sin t))\)
48. \(y=\frac{e^{-t/2}}{10}(5t+26)-\frac{1}{5}(3\cos t+\sin t)\)
49. \(y=\frac{1}{100}(3e^{3t}-e^{t/3}(3+310t))\)
50. \(y={3\over 2}e^{-7t/2}\cos {\sqrt {15}\over 2}t+{7\sqrt {15}\over 10}e^{-7t/2}\sin {\sqrt {15}\over 2}t\)
51. \(\frac{1}{a}e^{\frac{b}{a}t}f\left(\frac{t}{a}\right)\)