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I do not have an idea where to start to solve the following differential equation, so every tip is welcome.

$y' = \frac{x\sqrt{4+y^{2}}}{y(9+x^{2})} $

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    @JavierBadia - thanks, it's a little late here in Europe (2:44AM), therefore slower i think :D2012-07-19

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We write your equation as $ \frac{y}{\sqrt{4+y^2}}dy=\frac{x}{9+x^2}dx $ or equivalenlently, $ d(\sqrt{4+y^2})=d((1/2)\ln(9+x^2)). $ Hence, we get $ \sqrt{4+y^2}=\frac{1}{2}\ln(9+x^2)+C. $