# What is a solution to the differential equation  xy' = y?

May 5, 2018

$y = A x$

#### Explanation:

We have:

$x y ' = y$

Which we can write as:

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

Which is separable, so we can "separate the variables" to get:

$\ln | y | = \ln | x | + \ln A$

So that:

$\ln | y | = \ln A | x |$

$\therefore y = A x$