7: Section 2.4 Answers
- Page ID
- 103622
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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. \(y=\frac{1}{1-ce^{x}}\)
2. \(y=x^{2/7}(c-\ln |x|)^{1/7}\)
3. \(y=e^{2/x}(c-1/x)^{2}\)
4. \(y^{-3}=x+{1\over 3}+ce^{3x}\)
5. \(y=\pm\frac{\sqrt{2x+c}}{1+x^{2}}\)
6. \(e^{t/y}=ct\)
7. \(y=\pm (1-x^{2}+ce^{-x^{2}})^{-1/2}\)
8. \(y=\left[\frac{x}{3(1-x)+ce^{-x}} \right] ^{1/3}\)
9. \(y=\frac{2\sqrt{2}}{\sqrt{1-4x}}\)
10. \(y=\left[-1+\frac{3}{2}e^{-(x^{2}-1)/4} \right]^{-2}\)
11. \(y=\frac{1}{x(11-3x)^{1/3}}\)
12. \(y=(2e^{x}-1)^{2}\)
13. \(y^{-3}=-{9\over 5}x^{-1}+{49\over 5}x^{-6}\)
14. \(y=(2e^{12x}-1-12x)^{1/3}\)
15. \(y=\left[\frac{5x}{2(1+4x^{5})} \right]^{1/2}\)
16. \(y=(4e^{x/2}-x-2)^{2}\)
17. \(y=x(\ln |x|+c)\)
18. \(\ln |{y\over x}|-\ln |{y\over x}+1|=\ln |x|+c; \quad y=-x\)
19. \(y=\pm x(4\ln |x|+c)^{1/4}\)
20. \(y=x\sin ^{-1}(\ln |x|+c)\)
21. \(y=x\tan (\ln |x|+c)\)
22. \(4x=y(\ln |y|-c)^2\)
23. \(y=\pm x\sqrt{cx^{2}-1}\)
24. \(e^{(y/x)^2}=\ln |x|+c\)
25. \(y=-\frac{2x}{2\ln |x|+1}\)
26. \(y^3+3x^3\ln |x|=8x^3\)
27. \(y=x(3\ln x+27)^{1/3}\)
28. \(y=\frac{1}{x}\left(\frac{9-x^{4}}{2} \right)^{1/2}\)
29. \(\ln |x|=e^{y/x}-1\)
30. \(y=-x\)
31. \(y=-\frac{x(4x-3)}{(2x-3)}\)
32. \(y=x\sqrt{4x^{6}-1}\)
33. \(\tan ^{-1}\frac{y}{x}-\frac{1}{2}\ln (x^{2}+y^{2})=c\)
34. \((x+y)\ln |x|+y(1-\ln |y|)+cx=0\)
35. \((y+x)^{3}=3x^{3}(\ln |x|+c)\)
36. \((y+x)=c(y-x)^{3};\quad y=x;\quad y=-x\)
37. \(y^{2}(y-3x)=c;\quad y≡0;\quad y=3x\)
38. \((x-y)^{3}(x+y)=cy^{2}x^{4};\quad y=0;\quad y=x;\quad y=-x\)
39. \(\frac{y}{x}+\frac{y^{3}}{x^{3}}=\ln |x|+c\)
40. \(y=-x-1+\tan (x+c)\)
41. \(2y-2x+\sin 2(x+y)=c\)
42. \(4y-8x+12=(x+c)^2\)
43. \((x+y)^2=2x+c\)
44. \(\tan (x+y)-\sec (x+y)=x+c\)
45. \(-e^{-y+x-5}=x+c\)
46. \(-\cot (x+y)+\csc (x+y)=x+\sqrt{2}-1\)
47. \(4\ln |15x+10y+6|=10x-10y+4\ln 19\)