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Mathematics LibreTexts

Section 9.1 Answers

  • Page ID
    29615
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    2. \(y=2x^{2}-3x^{3}+\frac{1}{x}\)

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

    4. \(y_{i}=\frac{(x-x_{0})^{i-1}}{(i-1)!},\quad 1\leq i\leq n\)

    5. 

    b. \(y_{1}=-\frac{1}{2}x^{3}+x^{2}+\frac{1}{2x},\quad y_{2}=\frac{1}{3}x^{2}-\frac{1}{3x},\quad y_{3}=\frac{1}{4}x^{3}-\frac{1}{3}x^{2}+\frac{1}{12x}\)

    c. \(y=k_{0}y_{1}+k_{1}y_{2}+k_{2}y_{3}\)

    7. \(2e^{-x^{2}}\)

    8. \(\sqrt{2}K\cos x\)

    9.

    a. \(W(x)=2e^{3x}\)

    d. \(y=e^{x}(c_{1}+c_{2}x+c_{3}x^{2})\)

    10. 

    1. \(2\)
    2. \(-e^{3x}\)
    3. \(4\)
    4. \(4/x^{2}\)
    5. \(1\)
    6. \(2x\)
    7. \(2/x^{2}\)
    8. \(e^{x}(x^{2}-2x+2)\)
    9. \(-240/x^{5}\)
    10. \(6e^{2x}(2x-1)\)
    11. \(-128x\)

    24. 

    1. \(y'''=0\)
    2. \(xy'''-y''-xy'+y=0\)
    3. \((2x-3)y'''-2y''-(2x-5)y'=0\)
    4. \((x^{2}-2x+2)y'''-x^{2}y''+2xy'-2y=0\)
    5. \(x^{3}y'''+x^{2}y''-2xy'+2y=9\)
    6. \((3x-1)y'''-(12x-1)y''+9(x+1)y'-9y=0\)
    7. \(x^{4}y^{(4)}+5x^{3}y'''-3x^{2}y''-6xy'+6y=0\)
    8. \(x^{4}y^{(4)}+3x^{2}y'''-x^{2}y''+2xy'-2y=0\)
    9. \((2x-1)y^{(4)}-4xy'''+(5-2x)y''+4xy'-4y=0\)
    10. \(xy^{(4)}-y'''-4xy''+4y'=0\)