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Math Help - simple differential equation

  1. #1
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    simple differential equation

    I want to solve simple differential equation

    2x(1+sqrt(x^2-y)) = y'*sqrt(x^2-y)

    10x in advance
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  2. #2
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    Quote Originally Posted by pafpat View Post
    I want to solve simple differential equation

    2x(1+sqrt(x^2-y)) = y'*sqrt(x^2-y)

    10x in advance
    Well, there's probably some obviously simple approach. In the meantime:

    Make the substitution w^2 = x^2 - y \Rightarrow 2w \frac{dw}{dx} 2x - \frac{dy}{dx} \Rightarrow \frac{dy}{dx} = 2x - 2w \frac{dw}{dx}.

    Then after a little algebra the DE becomes -w^2 \frac{dw}{dx} = x which is seperable. Solve for w and then substitute back w^2 = x^2 - y.
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