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Mathematics LibreTexts

Section 9.4 Answers

  • Page ID
    30063
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    1. \(y_{p}=2x^{3}\)

    2. \(y_{p}=\frac{8}{105}x^{7/2}e^{-x^{2}}\)

    3. \(y_{p}=x\ln |x|\)

    4. \(y_{p}=-\frac{2(x^{2}+2)}{x}\)

    5. \(y_{p}=-\frac{xe^{-3x}}{64}\)

    6. \(y_{p}=-\frac{2x^{2}}{3}\)

    7. \(y_{p}=-\frac{e^{-x}(x+1)}{x}\)

    8. \(y_{p}=2x^{2}\ln |x|\)

    9. \(y_{p}=x^{2}+1\)

    10. \(y_{p}=\frac{2x^{2}+6}{3}\)

    11. \(y_{p}=\frac{x^{2}\ln |x|}{3}\)

    12. \(y_{p}=-x^{2}-2\)

    13. \(\frac{1}{4}x^{3}\ln |x|-\frac{25}{48}x^{3}\)

    14. \(y_{p}=\frac{x^{5/2}}{4}\)

    15. \(y_{p}=\frac{x(12-x^{2})}{6}\)

    16. \(y_{p}=\frac{x^{4}\ln |x|}{6}\)

    17. \(y_{p}=\frac{x^{3}e^{x}}{2}\)

    18. \(y_{p}=x^{2}\ln |x|\)

    19. \(y_{p}=\frac{xe^{x}}{2}\)

    20. \(y_{p}=\frac{3xe^{x}}{2}\)

    21. \(y_{p}=-x^{3}\)

    22. \(y=-x(\ln x)^{2}+3x+x^{3}-2x\ln x\)

    23. \(y=\frac{x^{3}}{2}(\ln |x|)^{2}+x^{2}-x^{3}+2x^{3}\ln |x|\)

    24. \(y=-\frac{1}{2}(3x+1)xe^{x}-3e^{x}-e^{2x}+4xe^{-x}\)

    25. \(y=\frac{3}{2}x^{4}(\ln x)^{2}+3x-x^{4}+2x^{4}\ln x\)

    26. \(y=-\frac{x^{4}+12}{6}+3x-x^{2}+2e^{x}\)

    27. \(y=\left(\frac{x^{2}}{3}-\frac{x}{2}\right)\ln |x|+4x-2x^{2}\)

    28. \(y=-\frac{xe^{x}(1+3x)}{2}+\frac{x+1}{2}-\frac{e^{x}}{4}+\frac{e^{3x}}{2}\)

    29. \(y=-8x+2x^{2}-2x^{3}+2e^{x}-e^{-x}\)

    30. \(y=3x^{2}\ln x-7x^{2}\)

    31. \(y=\frac{3(4x^{2}+9)}{2}+\frac{x}{2}-\frac{e^{x}}{2}+\frac{e^{-x}}{2}+\frac{e^{2x}}{4}\)

    32. \(y=x\ln x+x-\sqrt{x}+\frac{1}{x}+\frac{1}{\sqrt{x}}\)

    33. \(y=x^{3}\ln |x|+x-2x^{3}+\frac{1}{x}-\frac{1}{x^{2}}\)

    35. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{(x-t)}-3e^{-(x-t)}+2e^{-2(x-t)} }{6}F(t)dt\)

    36. \(y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{2}(2x+t)}{6xt^{3}}F(t)dt\)

    37. \(y_{p}=\int_{x_{0}}^{x}\frac{xe^{(x-t)}-x^{2}+x(t-1) }{t^{4}}F(t)dt\)

    38. \(y_{p}=\int_{x_{0}}^{x}\frac{x^{2}-t(t-2)-2te^{(x-t)}}{2x(t-1)^{2}}F(t)dt\)

    39. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}-2e^{(x-t)}+2e^{-(x-t)}-e^{-2(x-t)}}{12}F(t)dt\)

    40. \(y_{p}=\int_{x_{0}}^{x}\frac{(x-t)^{3}}{6x}F(t)dt\)

    41. \(y_{p}=\int_{x_{0}}^{x}\frac{(x+t)(x-t)^{3}}{12x^{2}t^{3}}F(t)dt\)

    42. \(y_{p}=\int_{x_{0}}^{x}\frac{e^{2(x-t)}(1+2x)+e^{-2(x-t)}(1-2t)-4x^{2}+4t^{2}-2}{32t^{2}}F(t)dt\)