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

Jul 20, 2016

$y = \ln x + x + C$

#### Explanation:

$y ' = \frac{1}{x} + 1$
$\int \setminus y ' \setminus \mathrm{dx} = \int \setminus \frac{1}{x} + 1 \setminus \mathrm{dx}$
$\implies \int \setminus \mathrm{dy} = \int \setminus \frac{1}{x} + 1 \setminus \mathrm{dx}$
$y = \ln x + x + C$