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Math Help - how to pick a variable here??

  1. #1
    MHF Contributor
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    how to pick a variable here??

    <br />
xyy'=\frac{x^2}{cos(\frac{y}{x})}+y^2<br />

    i know i need to look for a variable which both its derivative and him selft are present in the equation.
    i tried t=y/x
    but its derivative is not present in the equation

    ??
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  2. #2
    Super Member Matt Westwood's Avatar
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    This appears to be homogeneous if you divide all thru by xy.

    Then you'll have a function in y/x. Make the substitution z = y/x, substitute for dy/dx (it's z + x dz/dx) and you will find you have a diffeq with separable variables.
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