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Math Help - Interesting Equation

  1. #1
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    Interesting Equation

    (xe^(y/x)+ 2(x^2)y)dy − (ye^(y/x))dx = 0

    I've tried solving this equation with no luck. I have tried a variety of different ways but I end up with integrals that are impossible to solve.

    Any suggestions would be greatly appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by FatherMike View Post
    (xe^(y/x)+ 2(x^2)y)dy − (ye^(y/x))dx = 0

    I've tried solving this equation with no luck. I have tried a variety of different ways but I end up with integrals that are impossible to solve.

    Any suggestions would be greatly appreciated. Thanks!
    If you group the terms as follows

     <br />
(x \,dy - y \,dx) e^{y/x} + 2y\,dy = 0<br />

    then divide by x^2 so

     <br />
\frac{x\,dy - y\,dx}{x^2} e^{y/x} + 2y \, dy = 0<br />

    so

     <br />
d\left(\frac{y}{x} \right) e^{y/x} + d\left(y^2\right) = 0<br />

    which can be integrated giving

     <br />
e^{y/x} + y^2 = c.<br />
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