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Math Help - Substitution for diff. eq.

  1. #1
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    Substitution for diff. eq.

    Hi

    Having a bit of trouble with what the substition would be to solve this diff. Any ideas? Thanks.

    dy/dx = (xy)/(x^2 - y^2)
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Croc View Post
    Hi

    Having a bit of trouble with what the substition would be to solve this diff. Any ideas? Thanks.

    dy/dx = (xy)/(x^2 - y^2)
    divide the right hand side by x^2

    \frac{dy}{dx} = \displaystyle{\frac{\frac{xy}{x^2}}{\frac{x^2}{x^2  } - \frac{y^2}{x^2}}}

    \frac{dy}{dx} = \displaystyle{\frac{\frac{y}{x}}{1-\bigg(\frac{y}{x}\bigg)^2}}

    now let

    v = \frac{y}{x}

    and

    vx =y

    so

    v + \bigg(\frac{dv}{dx}\bigg)x = \frac{dy}{dx}

    now sub everything in and solve.
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