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Math Help - [SOLVED] Integrating Factor

  1. #1
    Member Altair's Avatar
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    Angry [SOLVED] Integrating Factor

    I want to find out the integrating factor of (y^4 + 2y)dx + (xy^3 + 2y^4 - 4x)dy = 0

    As M is y^4 + 2y and N is xy^3 + 2y^4 - 4x I took the partial derivative of N with respect to x and that of M with respect to y and then dividing by M I got :-

    \frac {(y^3 - 4) - (4y^3 + 2)}{y^4 +2y}

    Whereas the answer at the back is simply \frac{1}{y^3}.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Altair View Post
    I want to find out the integrating factor of (y^4 + 2y)dx + (xy^3 + 2y^4 - 4x)dy = 0

    As M is y^4 + 2y and N is xy^3 + 2y^4 - 4x I took the partial derivative of N with respect to x and that of M with respect to y and then dividing by M I got :-

    \frac {(y^3 - 4) - (4y^3 + 2)}{y^4 +2y}

    Whereas the answer at the back is simply \frac{1}{y^3}.

    \frac {(y^3 - 4) - (4y^3 + 2)}{y^4 +2y} \iff<br />
\frac{-3(y^3+2)}{y(y^3+2)}=\frac{-3}{y^3}

    so

    I(y)=\int \frac{-3}{y}dy=\frac{1}{y^3}

    Good luck.
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  3. #3
    Member Altair's Avatar
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    Or if there is a different method to solve this then please do tell about that.
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