A.2.6: Section 2.6 Answers
- Page ID
- 43756
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)3. \(\mu (x)=1/x^{2};\quad y=cx\text{ and }\mu (y)=1/y^{2};\quad x=cy\)
4. \(\mu (x)=x^{-3/2};\quad x^{3/2}y=c\)
5. \(\mu (y)=1/y^{3};\quad y^{3}e^{2x}=c\)
6. \(\mu (x)=e^{5x/2};\quad e^{5x/2}(xy+1)=c\)
7. \(\mu (x)=e^{x};\quad e^{x}(xy+y+x)=c\)
8. \(\mu (x)=x;\quad x^{2}y^{2}(9x+4y)=c\)
9. \(\mu (y)=y^{2};\quad y^{3}(3x^{2}y+2x+1)=c\)
10. \(\mu (y)=ye^{y};\quad e^{y}(xy^{3}+1)=c\)
11. \(\mu (y)=y^{2};\quad y^{3}(3x^{4}+8x^{3}y+y)=c\)
12.\(\mu (x)=xe^{x};\quad x^{2}y(x+1)e^{x}=c\)
13. \(\mu (x)=(x^{3}-1)^{-4/3};\quad xy(x^{3}-1)^{-1/3}=c\text{ and }x ≡ 1\)
14. \(\mu (y) = e^{y};\quad e^{y}(\sin x\cos y+y-1)=c\)
15. \(\mu (y)=e^{-y^{2}};xye^{-y^{2}}(x+y)=c\)
16. \(\frac{xy}{\sin y}=c\text{ and }y=k\pi (k=\text{integer})\)
17. \(\mu (x,y)=x^{4}y^{3};\quad x^{5}y^{4}\ln x=c\)
18. \(\mu (x,y)=1/xy;\quad |x|^{\alpha }|y|^{\beta }e^{\gamma x}e^{\delta y}=c\text{ and }x ≡ 0, y ≡ 0\)
19. \(\mu (x,y)=x^{-2}y^{-3};\quad 3x^{2}y^{2}+y=1+cxy^{2}\text{ and }x ≡ 0, y ≡ 0\)
20. \(\mu (x,y)=x^{-2}y^{-1};\quad -\frac{2}{x}+y^{3}+3\ln |y|=c\text{ and }x ≡ 0, y ≡ 0\)
21. \(\mu (x,y) = e^{ax}e^{by};\quad e^{ac}e^{by}\cos xy=c\)
22. \(\mu (x,y) = x^{-4}y^{-3}\text{ (and others) }xy=c\)
23. \(\mu (x,y) = xe^{y};\quad x^{2}ye^{y}\sin x=c\)
24. \(\mu (x,y) = 1/x^{2};\quad \frac{x^{3}y^{3}}{3}-\frac{y}{x}=c\)
25. \(\mu (x)=x+1;\quad y(x+1)^{2}(x+y)=c\)
26. \(\mu (x,y) = x^{2}y^{2};\quad x^{3}y^{3}(3x+2y^{2})=c\)
27. \(\mu (x,y) = x^{-2}y^{-2};\quad 3x^{2}y=cxy +2\text{ and }x ≡ 0, y ≡ 0\)