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Math Help - Differential equation

  1. #1
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    Differential equation

    Find the general solution of the equation x+2y\sqrt{x^{2}+1}\frac{dy}{dx}=0

    I then separated the variables:
     <br /> <br />
2ydy=\frac{-x}{\sqrt{x^2+1}}dx<br />

    I'm just struggling with the integration part.
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  2. #2
    o_O
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    I'm assuming it's the RHS causing you trouble: -\int \frac{x}{\sqrt{x^2+1}} \ dx

    Let: {\color{red}u = x^2 + 1} \ \Rightarrow \ du = 2x \ dx \ \Leftrightarrow \ {\color{blue}\frac{1}{2}du = xdx}

    So: -\int \frac{{\color{blue}x}}{\sqrt{{\color{red}x^2+1}}} \ {\color{blue}dx} = -{\color{blue}\frac{1}{2}} \int \frac{1}{\sqrt{{\color{red}u}}} {\color{blue}du} = -\frac{1}{2}\int u^{-\frac{1}{2}}du
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  3. #3
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    I got y^2=-\sqrt{x^2+1}+C

    Is this correct, and if so, how would you get it so its y= ?
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