# What is a solution to the differential equation (y+1)dy/dx=2x?

Aug 1, 2016

$y = \pm \sqrt{2 {x}^{2} + C} - 1$

#### Explanation:

$\left(y + 1\right) \frac{\mathrm{dy}}{\mathrm{dx}} = 2 x$

integrating wrt x
$\int \setminus \left(y + 1\right) \frac{\mathrm{dy}}{\mathrm{dx}} \setminus \mathrm{dx} = \int \setminus 2 x \setminus \mathrm{dx}$

$\int \setminus \left(y + 1\right) \setminus \mathrm{dy} = 2 \int \setminus x \setminus \mathrm{dx}$

$\frac{1}{2} {\left(y + 1\right)}^{2} = {x}^{2} + C$

${\left(y + 1\right)}^{2} = 2 {x}^{2} + C$

$y + 1 = \pm \sqrt{2 {x}^{2} + C}$

$y = \pm \sqrt{2 {x}^{2} + C} - 1$