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Math Help - Not by separating variables

  1. #1
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    Not by separating variables

    Here's the equation  \frac{dx}{\frac{ay}{x^2+y^2}}=\frac{dy}{\frac{ax}{  x^2+y^2}}
    how is this one done separating variables seems impossible
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  2. #2
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    Quote Originally Posted by phycdude View Post
    Here's the equation  \frac{dx}{\frac{ay}{x^2+y^2}}=\frac{dy}{\frac{ax}{  x^2+y^2}}
    how is this one done separating variables seems impossible
    Doesn't x^2+y^2 cancel in each term? Was this the original problem?
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  3. #3
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    Quote Originally Posted by Danny View Post
    Doesn't x^2+y^2 cancel in each term? Was this the original problem?
    well thats what beats me too , i have no idea whether that would be legitimate ,
    now this was not the question itself, i was just wondering, but here is what drove me to ask ,
    MathBin.net - Untitled
    if u like i can post the stuff here, im stumped.
    Last edited by phycdude; November 21st 2009 at 10:53 AM. Reason: Url
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  4. #4
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    Quote Originally Posted by phycdude View Post
    well thats what beats me too , i have no idea whether that would be legitimate ,
    now this was not the question itself, i was just wondering, but here is what drove me to ask ,
    MathBin.net - Untitled
    if u like i can post the stuff here, im stumped.
    Yes, of course that's legitmate. Your equation is simply [tex]\frac{dx}{y}= \frac{dy}{x}[quote] which is the same as xdx= ydy.
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  5. #5
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    [QUOTE=HallsofIvy;409885]Yes, of course that's legitmate. Your equation is simply [tex]\frac{dx}{y}= \frac{dy}{x}
    which is the same as xdx= ydy.
    thanks, well i was wondering since pathlines are given by  \frac{dx}{dt} = u and the same for v and w with dx replaced by dy and dz respectively , how would i integrate to obtain the trigonometric solutions here mathbin.net/37252
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