Skip to main content
Mathematics LibreTexts

11.52: A.8.3- Section 8.3 Answers

  • Page ID
    121450
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

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

    1. \(y=\frac{1}{6}e^{t}-\frac{9}{2}e^{-t}+\frac{16}{3}e^{-2t}\)

    2. \(y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}\)

    3. \(y=-\frac{23}{15}e^{-2t}+\frac{1}{3}e^{t}+\frac{1}{5}e^{3t}\)

    4. \(y=-\frac{1}{4}e^{2t}+\frac{17}{20}e^{-2t}+\frac{2}{5}e^{3t}\)

    5. \(y=\frac{11}{15}e^{-2t}+\frac{1}{6}e^{t}+\frac{1}{10}e^{3t}\)

    6. \(y=e^{t}+2e^{-2t}-2e^{-t}\)

    7. \(y=\frac{5}{3}\sin t-\frac{1}{3}\sin 2t\)

    8. \(y=4e^{t}-4e^{2t}+e^{3t}\)

    9. \(y=-\frac{7}{2}e^{2t}+\frac{13}{3}e^{t}+\frac{1}{6}e^{4t}\)

    10. \(y=\frac{5}{2}e^{t}-4e^{2t}+\frac{1}{2}e^{3t}\)

    11. \(y=\frac{1}{3}e^{t}-2e^{-t}+\frac{5}{3}e^{-2t}\)

    12. \(y=2-e^{-2t}+e^{t}\)

    13. \(y=1-\cos 2t+\frac{1}{2}\sin 2t\)

    14. \(y=-\frac{1}{3}+\frac{8}{15}e^{3t}+\frac{4}{5}e^{-2t}\)

    15. \(y=\frac{1}{6}e^{t}-\frac{2}{3}e^{-2t}+\frac{1}{2}e^{-t}\)

    16. \(y=-1+e^{t}+e^{-t}\)

    17. \(y=\cos 2t-\sin 2t+\sin t\)

    18. \(y=\frac{7}{3}-\frac{7}{2}e^{-t}+\frac{1}{6}e^{3t}\)

    19. \(y=1+\cos t\)

    20. \(y=t+\sin t\)

    21. \(y=t-6\sin t+\cos t+\sin 2t\)

    22. \(y=e^{-t}+4e^{-2t}-4e^{-3t}\)

    23. \(y=-3\cos t-2\sin t+e^{-t}(2+5t)\)

    24. \(y=-\sin t-2\cos t+3e^{3t}+e^{-t}\)

    25. \(y=(3t+4)\sin t-(2t+6)\cos t\)

    26. \(y=-(2t+2)\cos 2t+\sin 2t+3\cos t\)

    27. \(y=e^{t}(\cos t-3\sin t)+e^{3t}\)

    28. \(y=-1+t+e^{-t}(3\cos t-5\sin t)\)

    29. \(y=4\cos t-3\sin t-e^{t}(3\cos t-8\sin t)\)

    30. \(y=e^{-t}-2e^{t}+e^{-2t}(\cos 3t- 11/3\sin 3t)\)

    31. \(y=e^{-t}(\sin t-\cos t)+e^{-2t}(\cos t+4\sin t)\)

    32. \(y=\frac{1}{5}e^{2t}-\frac{4}{3}e^{t}+\frac{32}{15}e^{-t/2}\)

    33. \(y=\frac{1}{7}e^{2t}-\frac{2}{5}e^{t/2}+\frac{9}{35}e^{-t/3}\)

    34. \(y=e^{-t/2}(5\cos (t/2)-\sin (t/2))+2t-4\)

    35. \(y=\frac{1}{17}(12\cos t+20\sin t-3e^{t/2}(4\cos t+\sin t))\)

    36. \(y=\frac{e^{-t/2}}{10}(5t+26)-\frac{1}{5}(3\cos t+\sin t)\)

    37. \(y=\frac{1}{100}(3e^{3t}-e^{t/3}(3+310t))\)


    This page titled 11.52: A.8.3- Section 8.3 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

    • Was this article helpful?