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Math Help - dy/dx = (y^2 - x^2)/xy

  1. #1
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    dy/dx = (y^2 - x^2)/xy

    I need to find the general solution, in explicit form of this equation:

    dy/dx = (y^2 - x^2)/xy

    Let u = xy

    y =u/x

    du/dx = y + dy/dx

    So i then get;

    du/dx - (u/x) = [(u/x)^2 - x^2]/u

    Is this correct so far? Could anyone tell me where to go next?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Mcoolta View Post
    Is this correct so far? Could anyone tell me where to go next?
    Yes, it is correct, but the substitution y=ux is better. You will obtain a separated variables equation.

    Fernando Revilla
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  3. #3
    A Plied Mathematician
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    The original DE is also Bernoulli.
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  4. #4
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    Ok so using y = ux

    dy/dx = x(du/dx) + u

    x(du/dx) + u = [(ux)^2 - x^2]/x^2u

    After rearranging, i got

    X(du/dx) = -1/u

    Then:

    1/x dx = -u du

    Is this correct? Thanks
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