# What is a solution to the differential equation x dy/dx=1/y?

What is a solution to the differential equation $x\frac{dy}{dx}=\frac{1}{y}$?
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Isaiah Haynes
this is separable
$x\frac{dy}{dx}=\frac{1}{y}$
$y\frac{dy}{dx}=\frac{1}{x}$
$\int ydy=\int \frac{1}{x}dx$
$\frac{{y}^{2}}{2}=\mathrm{ln}x+C$
${y}^{2}=2\mathrm{ln}x+C={\mathrm{ln}x}^{2}+C$
$y=±\sqrt{{\mathrm{ln}x}^{2}+C}$