19: Section 5.6 Answers
- Page ID
- 103638
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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. \(y=c_1\cos 3x+c_2\sin 3x+\frac{-\cos 3x\ln |\sec 3x+\tan 3x|}{9}\)
2. \(y= c_1\cos 2x+c_2\sin 2x-\frac{\sin 2x\ln |\cos 2x|}{4}+\frac{x\cos 2x}{2}\)
3. \(y = c_1e^x+c_2e^{2x}+4e^{x} (1 + e^{x} ) \ln(1 + e^{−x} )\)
4. \(y =c_1e^x\cos x+c_2e^x\sin x+3e^{x}+\cos x \ln | \cos x| + x \sin x\)
5. \(y=c_1e^x+c_2xe^x+\frac{8}{5}x^{7/2}e^{x}\)
6. \(y=c_1e^x+c_2e^{-x}+e^{x}\ln (1-e^{-2x})-e^{-x}\ln (e^{2x}-1)\)
7. \(y=c_1x+c_2{1\over x}+\frac{2(x^{2}-3)}{3}\)
8. \(y=c_1e^x+c_2{e^x\over x}+\frac{e^{2x}}{x}\)
9. \(y= c_1x^{1/2} e^x+c_2x^{-1/2}e^x +x^{1/2}e^{x}\ln x\)
10. \(y= c_1e^{-x^2}+c_2xe^{-x^2}+e^{-x(x+2)}\)
11. \(y= c_1x^2+c_2x^3 -4x^{5/2}\)
12. \(y=c_1x+c_2x^3 −2x^{2} \sin x−2x \cos x\)
13. \(y= c_1e^{-x}+c_2xe^x -\frac{xe^{-x}(x+1)}{2}\)
14. \(y= c_1\cos\sqrt x+c_2\sin\sqrt x -\frac{\sqrt{x}\cos\sqrt{x}}{2}\)
15. \(y= c_1e^x+c_2x^3e^x+ \frac{3x^{4}e^{x}}{2}\)
16. \(y= c_1x^a+c_2x^a \ln x +x^{a+1}\)
17. \(y=c_1 x\cos x+c_2x\sin x +\frac{x^{2}\sin x}{2}\)
18. \(y= c_1e^{x^2}+c_2e^{-x^2} -2x^{2}\)
19. \(y=c_1 e^{-x}+c_2e^{-x}\cos x -e^{-x}\sin x\)
20. \(y= c_1\sqrt xe^{2x}+c_2\sqrt xe^{-2x} -\frac{\sqrt{x}}{2}\)
21. \(y= c_1\sqrt x\sin x+c_2\sqrt x\cos x +\frac{x^{3/2}}{4}\)
22. \(y= c_1xe^x+c_2xe^{-x} -3x^{2}\)
23. \(y= c_1xe^x+c_2x^2e^x +\frac{x^{3}e^{x}}{2}\)
24. \(y= c_1{1\over x}++c_2x^3 -\frac{4x^{3/2}}{15}\)
25. \(y= c_1x^2+c_2x^2e^x +x^{3}e^{x}\)
26. \(y= c_1x^2e^x+c_2x^3e^x +xe^{x}\)
27. \(y= c_1x^2\cos x+c_2x^2\sin x +x^{2}\)
28. \(y =c_1 x+c_2e^x +xe^{x} (x − 2)\)
29. \(y= c_1\sqrt x+c_2\sqrt xe^x +\sqrt{x}e^{x}(x-1)/4\)
30. \(y=\frac{e^{2x}(3x^{2}-2x+6)}{6}+\frac{xe^{-x}}{3}\)
31. \(y = (x − 1)^{2} \ln(1 − x) + 2x^{2} − 5x + 3\)
32. \(y = (x^{2}−1)e^{x}−5(x−1)\)
33. \(y=\frac{x(x^{2}+6)}{3(x^{2}-1)}\)
34. \(y=-\frac{x^{2}}{2}+x+\frac{1}{2x^{2}}\)
35. \(y=\frac{x^{2}(4x+9)}{6(x+1)}\)
36. \(y=c_1e^x\cos 3x+c_2e^x\sin 3x+{2\over 17}\cos x+{9\over 17}\sin x-{1\over 27}e^x\cos 3x\ln |\sec 3x+\tan 3x|\)
37. \(y=c_1\cos x+c_2\sin x-{1\over 2}x\cos x+x\sin x+\cos x\ln |\cos x|\)
38. \(y=c_1e^{-x}+c_2e^{-2x}+3x^2-9x+{21\over 2}-e^{-2x}\sin e^x+(e^{-x}+e^{-2x})\ln (1+e^x)\)
39. \(y=c_1e^x+c_2xe^x+x^3+6x^2+22x+32-{1\over 2}e^x\ln(1+x^2)+xe^x\tan^{-1} x \)
40. \(y=c_1e^x+c_2xe^x+{1\over 2}x^2e^x+{1\over 2}x^2e^x\tan^{-1} x-{1\over 2}e^x\tan^{-1} x-{1\over 2}xe^x\ln (1+x^2)\)