# What is the general solution of the differential equation? :  dy/dx = 1/x^2

Feb 7, 2018

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

#### Explanation:

We have:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{x} ^ 2$

This is a First Order Separable Ordinary Differential Equation. We can "separate the variables" to get:

$\int \setminus \mathrm{dy} = \int \setminus \frac{1}{x} ^ 2 \setminus \mathrm{dx}$

Both integrals are standard calculus results , so integrating we get:

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

Which is the General Solution