# How to you find the general solution of dy/dx=(x-2)/x?

Nov 29, 2016

The equation is separable so you separate the variables and integrate both members of the equation

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x - 2}{x}$

$\mathrm{dy} = \frac{x - 2}{x} \mathrm{dx}$

$\int \mathrm{dy} = \int \frac{x - 2}{x} \mathrm{dx}$

$y = \int \mathrm{dx} - 2 \int \frac{\mathrm{dx}}{x}$

$y = x - 2 \ln x + C$