# How do you find the general solution of the differential equation dy/dx=2x^-3?

Nov 11, 2016

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

#### Explanation:

This is a First Order separable DE, so we can rearrange and separate the variables as follows:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 {x}^{-} 3$
$\therefore \int \mathrm{dy} = \int 2 {x}^{-} 3 \mathrm{dx}$

Integrating gives:

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