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Mathematics LibreTexts

Section 5.4 Answers

  • Page ID
    28910
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    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.

    1. \(y=e^{-x}\left(\frac{4}{3}x^{3/2}+c_{1}x+c_{2} \right)\)
    2. \(y=e^{-3x}\left[\frac{x^{2}}{4}(2\ln x-3)+c_{1}x+c_{2} \right]\)
    3. \(y=e ^{2x} [(x + 1) \ln |x + 1| + c_{1}x + c_{2}]\)
    4. \(y=e^{-x/2}\left(x\ln |x| +\frac{x^{3}}{6}+c_{1}x+c_{2} \right)\)

    39. 

    1. \(e^{x}(3+x)+c\)
    2. \(-e^{-x}(1+x)^{2}+c\)
    3. \(-\frac{e^{-2x}}{8}(3+6x+6x^{2}=4x^{3})+c\)
    4. \(e^{x}(1 + x^{2} ) + c\)
    5. \(e^{3x} (−6 + 4x + 9x^{2} ) + c\)
    6. \(−e^{−x} (1 − 2x^{3} + 3x^{4} ) + c\)

    40. \(\frac{(-1)^{k}k!e^{\alpha x}}{\alpha ^{k+1}}\sum_{r=0}^{k}\frac{(-\alpha x)^{r}}{r!}+c\)