A.2.5: Section 2.5 Answers
- Page ID
- 43755
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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. \(2x^{3}y^{2}=c\)
2. \(3y\sin x+2x^{2}e^{x}+3y=c\)
3. Not exact
4. \(x^{2}-2xy^{2}+4y^{3}=c\)
5. \(x+y=c\)
6. Not exact
7. \(2y^{2}\cos x+3xy^{3}-x^{2}=c\)
8. Not exact
9. \(x^{3}+x^{2}y+4xy^{2}+9y^{2}=c\)
10. Not exact
11. \(\ln |xy|+x^{2}+y^{2}=c\)
12. Not exact
13. \(x^{2}+y^{2}=c\)
14. \(x^{2}y^{2}e^{x}+2y+3x^{2}=c\)
15. \(x^{3}e^{x^{2}+y}-4y^{3}+2x^{2}=c\)
16. \(x^{4}e^{xy}+3xy=c\)
17. \(x^{3}\cos xy+4y^{2}+2x^{2}=c\)
18. \(y=\frac{x+\sqrt{2x^{2}+3x-1}}{x^{2}}\)
19. \(y=\sin x-\sqrt{1-\frac{\tan x}{2}}\)
20. \(y=\left(\frac{e^{x}-1}{e^{x}+1} \right)^{1/3}\)
21. \(y=1+2\tan x\)
22. \(y=\frac{x^{2}-x+6}{(x+2)(x-3)}\)
23. \(\frac{7x^{2}}{2}+4xy+\frac{3y^{2}}{2}=c\)
24. \((x^{4}y^{2}+1)e^{x}+y^{2}=c\)
29.
- \(M(x,y)=2xy+f(x)\)
- \(M(x,y)=2(\sin x+x\cos x)(y\sin y +\cos y)+f(x)\)
- \(M(x,y) = ye^{x}-e^{y}\cos x+f(x)\)
30.
- \(N(x,y)=\frac{x^{4}y}{2}+x^{2}+6xy+g(y)\)
- \(N(x,y)=\frac{x}{y}+2y\sin x+g(y)\)
- \(N(x,y)=x(\sin y+y\cos y)+g(y)\)
33. \(B=C\)
34. \(B=2D,\quad E=2C\)
37.
- \(2x^{2}+x^{4}y^{4}+y^{2}=c\)
- \(x^{3}+3xy^{2}=c\)
- \(x^{3}+y^{2}+2xy=c\)
38. \(y=-1-\frac{1}{x^{2}}\)
39. \(y=x^{3}\left(\frac{-3(x^{2}+1)+\sqrt{9x^{4}+34x^{2}+21}}{2} \right)\)
40. \(y=-e^{-x^{2}}\left(\frac{2x+\sqrt{9-5x^{2}}}{3} \right)\)
44.
- \(G(x,y)=2xy+c\)
- \(G(x,y)=e^{x}\sin y+c\)
- \(G(x,y)=3x^{2}y-y^{3}+c\)
- \(G(x,y)=-\sin x\sinh y+c\)
- \(G(x,y)=\cos x\sinh y+c\)