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Mathematics LibreTexts

Section 2.6 Answers

  • Page ID
    28706
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    3. \(\mu (x)=1/x^{2};\quad y=cx\text{ and }\mu (y)=1/y^{2};\quad x=cy\)

    4. \(\mu (x)=x^{-3/2};\quad x^{3/2}y=c\)

    5. \(\mu (y)=1/y^{3};\quad y^{3}e^{2x}=c\)

    6. \(\mu (x)=e^{5x/2};\quad e^{5x/2}(xy+1)=c\)

    7. \(\mu (x)=e^{x};\quad e^{x}(xy+y+x)=c\)

    8. \(\mu (x)=x;\quad x^{2}y^{2}(9x+4y)=c\)

    9. \(\mu (y)=y^{2};\quad y^{3}(3x^{2}y+2x+1)=c\)

    10. \(\mu (y)=ye^{y};\quad e^{y}(xy^{3}+1)=c\)

    11. \(\mu (y)=y^{2};\quad y^{3}(3x^{4}+8x^{3}y+y)=c\)

    12.\(\mu (x)=xe^{x};\quad x^{2}y(x+1)e^{x}=c\)

    13. \(\mu (x)=(x^{3}-1)^{-4/3};\quad xy(x^{3}-1)^{-1/3}=c\text{ and }x ≡ 1\)

    14. \(\mu (y) = e^{y};\quad e^{y}(\sin x\cos y+y-1)=c\)

    15. \(\mu (y)=e^{-y^{2}};xye^{-y^{2}}(x+y)=c\)

    16. \(\frac{xy}{\sin y}=c\text{ and }y=k\pi (k=\text{integer})\)

    17. \(\mu (x,y)=x^{4}y^{3};\quad x^{5}y^{4}\ln x=c\)

    18. \(\mu (x,y)=1/xy;\quad |x|^{\alpha }|y|^{\beta }e^{\gamma x}e^{\delta y}=c\text{ and }x ≡ 0, y ≡ 0\)

    19. \(\mu (x,y)=x^{-2}y^{-3};\quad 3x^{2}y^{2}+y=1+cxy^{2}\text{ and }x ≡ 0, y ≡ 0\)

    20. \(\mu (x,y)=x^{-2}y^{-1};\quad -\frac{2}{x}+y^{3}+3\ln |y|=c\text{ and }x ≡ 0, y ≡ 0\)

    21. \(\mu (x,y) = e^{ax}e^{by};\quad e^{ac}e^{by}\cos xy=c\)

    22. \(\mu (x,y) = x^{-4}y^{-3}\text{ (and others) }xy=c\)

    23. \(\mu (x,y) = xe^{y};\quad x^{2}ye^{y}\sin x=c\)

    24. \(\mu (x,y) = 1/x^{2};\quad \frac{x^{3}y^{3}}{3}-\frac{y}{x}=c\)

    25. \(\mu (x)=x+1;\quad y(x+1)^{2}(x+y)=c\)

    26. \(\mu (x,y) = x^{2}y^{2};\quad x^{3}y^{3}(3x+2y^{2})=c\)

    27. \(\mu (x,y) = x^{-2}y^{-2};\quad 3x^{2}y=cxy +2\text{ and }x ≡ 0, y ≡ 0\)