20: Section 5.7 Answers
- Page ID
- 103639
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \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. \(y=x_{1}x^{-4}+c_{2}x^{-2}\)
2. \(y=c_{1}x+c_{2}x^{7}\)
3. \(y = x(c_{1} + c_{2} \ln x)\)
4. \(y = x^{−2} (c_{1} + c_{2} \ln x)\)
5. \(y = c_{1} \cos (\ln x) + c_{2} \sin (\ln x)\)
6. \(y = x^{2} [c_{1} \cos (3 \ln x) + c_{2} \sin (3 \ln x)]\)
7. \(y=c_{1}x+\frac{c_{2}}{x^{3}}\)
8. \(y = c_{1}x^{2/3} + c_{2}x^{3/4}\)
9. \(y = x^{−1/2} (c_{1} + c_{2} \ln x)\)
10. \(y = c_{1}x+c_{2}x^{1/3}\)
11. \(y = c_{1}x^{2}+c_{2}x^{1/2}\)
12. \(y =\frac{1}{x} [c_{1} \cos (2 \ln x) + c_{2} \sin (2 \ln x]\)
13. \(y = x^{−1/3} (c_{1} + c_{2} \ln x)\)
14. \(y = x [c_{1} \cos (3 \ln x) + c_{2} \sin (3 \ln x)]\)
15. \(y=c_{1}x^{3}+\frac{x_{2}}{x^{2}}\)
16. \(y=\frac{c_{1}}{x}+c_{2}x^{1/2}\)
17. \(y=x^{2}(c_{1}+c_{2}\ln x)\)
18. \(y=\frac{1}{x^{2}}\left[c_{1}\cos\left(\frac{1}{\sqrt{2}}\ln x \right)+c_{2}\sin\left(\frac{1}{\sqrt{2}}\ln x \right) \right]\)
19. \(y=c_1x^{-1}+c_2x^2\)
20. \(y=c_1+c_2\ln x\)
21. \(y=c_1\cos (2\ln x)+c_2\sin (2\ln x)\)
22. \(y=c_1x^{2-\sqrt 6}+c_2x^{2+\sqrt 6}\)
23. \(y=c_1\cos ({1\over 5}\ln x)+c_2\sin ({1\over 5}\ln x)\)
24. \(y=c_1x^{-2}+c_2x^{-2}\ln x\)
25. \(y=c_1x^{-1/2}\cos ({\sqrt 3\over 6}\ln x)+c_2x^{-1/2}\sin ({\sqrt 3\over 6}\ln x)\)
26. \(y=c_1x^{-3}+c_2x^1\)
27. \(y=c_1x^{(-3+\sqrt 5)/ 2}+c_2x^{(-3-\sqrt 5)/ 2}\)
28. \(y=c_1\cos({1\over 2}\ln x)+c_2\sin({1\over 2}\ln x)\)
29. \(y=c_1+c_2x^5+{1\over 5}x^5\ln x\)
30. \(y=c_1x+c_2x\ln x+x\ln^2 x\)
31. \(y=c_1x^{-1}+c_2x^3-{2\over 3}x^2\)
32. \(y=c_1x^{-1}+c_2x^3+{1\over 2}x^3\ln x\)
33. \(y=c_1x^2+c_2x^3+x^4-x^2\ln x\)
34. \(y=c_1x+c_2x^3+2x^2e^x-2xe^x\)
35. \(y=c_1x+c_2x\ln x+2+\ln x\)
36. \(y=c_1x^{-1/2}+c_2x^{-1}+{1\over 15}x^2+{1\over 6}x\)
37. \(y=c_1x^{-2}+c_2x^{-2}\ln x+{2\over 25}x^3\)
38. \(y=c_1x^{-1}+c_2x^{-8}+{1\over 30}x^2\)
39. \(y=c_1x^2+c_2x^3+{1\over 3}\ln x+{5\over 18}\)
40. \(y=c_1x^2\cos (3\ln x)+c_2x^2\sin (3\ln x)+{3\over 10}x+{4\over 13}\)
41. \(y=2-2x^{-2}\)
42. \(y=16x^2-2x^4\)
43. \(y=\cos (\ln x)+2\sin (\ln x)\)
44. \(y=5x^2-7x^2\ln x\)
45. \(y=x^{-1}\ln x\)
46. \(y={3\over 4}-\ln x+{1\over 4}x^2\)
47. \(y={1\over 16}x^2-{1\over 2}x^4+x^6\)
48. \(y=ex-ex^3+2x^2e^x-2xe^x\)
49. \(y=x\ln x+2+\ln x\)
51. \(y=2\sqrt {-x}-5\sqrt {-x}\ln (-x)\)
52. \(y=6x^2+2x^3\)