A.5.4: Section 5.4 Answers
- Page ID
- 43768
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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. \(y_{p}=e^{3x}\left(-\frac{1}{4}+\frac{x}{2} \right)\)
2. \(y_{p}=e^{-3x}\left(1-\frac{x}{4}\right)\)
3. \(y_{p}=e^{x}\left(2-\frac{3x}{4}\right)\)
4. \(y_{p} = e^{2x} (1−3x+x^{2})\)
5. \(y_{p} = e^{−x} (1+x^{2} )\)
6. \(y_{p} = e^{x} (−2+x+ 2x^{2} )\)
7. \(y_{p}=xe^{-x}\left(\frac{1}{6}+\frac{x}{2} \right)\)
8. \(y_{p} = xe^{x} (1 + 2x)\)
9. \(y_{p}=xe^{3x}\left(-1+\frac{x}{2} \right)\)
10. \(y_{p} = xe^{2x} (−2+x)\)
11. \(y_{p}=x^{2}e^{-x}\left(1+\frac{x}{2} \right)\)
12. \(y_{p}=x^{2}e^{x}\left(\frac{1}{2}-x \right)\)
13. \(y_{p}=\frac{x^{2}e^{2x}}{2}(1-x+x^{2})\)
14. \(y_{p}=\frac{x^{2}e^{-x/3}}{27}(3-2x+x^{2})\)
15. \(y=\frac{e^{3x}}{4}(-1+2x)+c_{1}e^{x}+c_{2}e^{2x}\)
16. \(y=e^{x}(1-2x)+c_{1}e^{2x}+c_{2}e^{4x}\)
17. \(y=\frac{e^{2x}}{5}(1-x)+e^{-3x}(c_{1}+c_{2}x)\)
18. \(y = xe^{x} (1 − 2x) + c_{1}e^{x} + c_{2}e^{−3x}\)
19. \(y = e^{x} \left[ x^{2} (1 − 2x) + c_{1} + c_{2}x\right ]\)
20. \(y = −e^{2x} (1 + x) + 2e^{−x} − e^{5x}\)
21. \(y = xe^{2x} + 3e^{x} − e^{−4x}\)
22. \(y = e ^{-x} (2 + x − 2x^{2}) − e^{−3x}\)
23. \(y = e ^{-2x} (3 − x) − 2e^{5x} \)
24. \(y_{p}=-\frac{e^{x}}{3}(1-x)+e^{-x}(3+2x)\)
25. \(y_{p} = e^{x} (3 + 7x) + xe^{3x}\)
26. \(y_{p}= x^{3} e^{4x} + 1 + 2x + x^{2}\)
27. \(y_{p} = xe^{2x} (1 − 2x) + xe^{x}\)
28. \(y_{p} = e^{x} (1 + x) + x^{2} e^{−x}\)
29. \(y_{p} = x^{2} e^{−x} + e^{3x} (1 − x^{2} )\)
31. \(y_{p} = 2e^{2x}\)
32. \(y_{p}=5xe^{4x}\)
33. \(y_{p}=x^{2}e^{4x}\)
34. \(y_{p}=-\frac{e^{3x}}{4}(1+2x-2x^{2})\)
35. \(y_{p}=xe^{3x}(4-x+2x^{2})\)
36. \(y_{p} = x^{2} e^{−x/2} (−1 + 2x + 3x^{2} )\)
37.
- \(y=e^{-x}\left(\frac{4}{3}x^{3/2}+c_{1}x+c_{2} \right)\)
- \(y=e^{-3x}\left[\frac{x^{2}}{4}(2\ln x-3)+c_{1}x+c_{2} \right]\)
- \(y=e ^{2x} [(x + 1) \ln |x + 1| + c_{1}x + c_{2}]\)
- \(y=e^{-x/2}\left(x\ln |x| +\frac{x^{3}}{6}+c_{1}x+c_{2} \right)\)
39.
- \(e^{x}(3+x)+c\)
- \(-e^{-x}(1+x)^{2}+c\)
- \(-\frac{e^{-2x}}{8}(3+6x+6x^{2}=4x^{3})+c\)
- \(e^{x}(1 + x^{2} ) + c\)
- \(e^{3x} (−6 + 4x + 9x^{2} ) + c\)
- \(−e^{−x} (1 − 2x^{3} + 3x^{4} ) + c\)
40. \(\frac{(-1)^{k}k!e^{\alpha x}}{\alpha ^{k+1}}\sum_{r=0}^{k}\frac{(-\alpha x)^{r}}{r!}+c\)