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

Jul 19, 2016

$y = x + \ln x + C$

#### Explanation:

This differential equation is separable.

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

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

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

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

$y = x + \ln x + C$