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Math Help - Equation Help

  1. #1
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    Equation Help

    (x-y)y'=(x+y)

    I've tried v=y/x and v=x-y, and both times it has just ended up as a mess.
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  2. #2
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    Re: Equation Help

    the solution Mathematica is pumping out seems to indicate that v=y/x was the right way to go.

    you can certainly separate the equation that way

    $$(x-y)y'=(x+y)$$
    $$v=\frac{y}{x}$$
    $$y=v x$$
    $$y'=x v'+v$$
    $$(x-v x)(x v'+v)=(x+v x)$$
    $$v x - v^2 x+x^2 v' - v x^2 v' = x + v x$$
    $$x^2(v' - v v')=x(1+v^2)$$
    $$x v'(1-v)=(1+v^2)$$
    $$\frac{1-v}{1+v^2}dv=\frac{dx}{x}$$
    Last edited by romsek; February 23rd 2014 at 02:24 PM.
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