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$$yy'+\frac yx+k=0$$

How to solve this differential equation for $y$ in terms of $x$ and $k$ where $k$ is a parameter of $x$?

$y(x)=y$ is a function and $x(k)=x$ is a gamma function

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What have you tried? –  Tom Oldfield Dec 30 '12 at 20:40
    
@TomOldfield - I can't figure it out with my high school calculus knowledge –  Victor Dec 30 '12 at 20:44
    
So is $y$ a function of $x$ and $k$, or is $y$ a function of $x$ with parameter $k$? –  Daryl Dec 30 '12 at 22:25
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@Victor If both $x(k)$ and $y(x)$ are unknown, then I suspect that this problem is ill-posed. –  Daryl Dec 31 '12 at 0:07
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The letter $k$ denotes a parameter, not a variable. - The ODE in question is equation $1\cdot237$ in Kamke's classical catalogue (here $a=0$, $b=1$, $c=k$). The prospects for a simple explicit solution are not excellent. –  Christian Blatter Dec 31 '12 at 16:37

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