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

Jul 7, 2016

$y = \pm \sqrt{\ln {x}^{2} + C}$

#### Explanation:

this is separable

$x \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{y}$

$y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{x}$

$\int y \mathrm{dy} = \int \frac{1}{x} \mathrm{dx}$

${y}^{2} / 2 = \ln x + C$

${y}^{2} = 2 \ln x + C = \ln {x}^{2} + C$

$y = \pm \sqrt{\ln {x}^{2} + C}$