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

Nov 16, 2016

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

#### Explanation:

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

This is a First Order Separable Differential Equation, we can "separate the variables" to give;

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

Integrating we get:

$\frac{1}{2} {y}^{2} = \frac{1}{2} {x}^{2} + A$
$\therefore {y}^{2} = {x}^{2} + 2 A$
$\therefore {y}^{2} = {x}^{2} + C$