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Mathematics LibreTexts

Section 2.5 Answers

  • Page ID
    28705
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    1. \(2x^{3}y^{2}=c\)

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

    3. Not exact

    4. \(x^{2}-2xy^{2}+4y^{3}=c\)

    5. \(x+y=c\)

    6. Not exact

    7. \(2y^{2}\cos x+3xy^{3}-x^{2}=c\)

    8. Not exact

    9. \(x^{3}+x^{2}y+4xy^{2}+9y^{2}=c\)

    10. Not exact

    11. \(\ln |xy|+x^{2}+y^{2}=c\)

    12. Not exact

    13. \(x^{2}+y^{2}=c\)

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

    15. \(x^{3}e^{x^{2}+y}-4y^{3}+2x^{2}=c\)

    16. \(x^{4}e^{xy}+3xy=c\)

    17. \(x^{3}\cos xy+4y^{2}+2x^{2}=c\)

    18. \(y=\frac{x+\sqrt{2x^{2}+3x-1}}{x^{2}}\)

    19. \(y=\sin x-\sqrt{1-\frac{\tan x}{2}}\)

    20. \(y=\left(\frac{e^{x}-1}{e^{x}+1} \right)^{1/3}\)

    21. \(y=1+2\tan x\)

    22. \(y=\frac{x^{2}-x+6}{(x+2)(x-3)}\)

    23. \(\frac{7x^{2}}{2}+4xy+\frac{3y^{2}}{2}=c\)

    24. \((x^{4}y^{2}+1)e^{x}+y^{2}=c\)

    29. 

    1. \(M(x,y)=2xy+f(x)\)
    2. \(M(x,y)=2(\sin x+x\cos x)(y\sin y +\cos y)+f(x)\)
    3. \(M(x,y) = ye^{x}-e^{y}\cos x+f(x)\)

    30. 

    1. \(N(x,y)=\frac{x^{4}y}{2}+x^{2}+6xy+g(y)\)
    2. \(N(x,y)=\frac{x}{y}+2y\sin x+g(y)\)
    3. \(N(x,y)=x(\sin y+y\cos y)+g(y)\)

    33. \(B=C\)

    34. \(B=2D,\quad E=2C\)

    37. 

    1. \(2x^{2}+x^{4}y^{4}+y^{2}=c\)
    2. \(x^{3}+3xy^{2}=c\)
    3. \(x^{3}+y^{2}+2xy=c\)

    38. \(y=-1-\frac{1}{x^{2}}\)

    39. \(y=x^{3}\left(\frac{-3(x^{2}+1)+\sqrt{9x^{4}+34x^{2}+21}}{2} \right)\)

    40. \(y=-e^{-x^{2}}\left(\frac{2x+\sqrt{9-5x^{2}}}{3} \right)\)

    44. 

    1. \(G(x,y)=2xy+c\)
    2. \(G(x,y)=e^{x}\sin y+c\)
    3. \(G(x,y)=3x^{2}y-y^{3}+c\)
    4. \(G(x,y)=-\sin x\sinh y+c\)
    5. \(G(x,y)=\cos x\sinh y+c\)