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

##### 1 Answer

May 5, 2018

# y = Ax #

#### Explanation:

We have:

# xy' = y #

Which we can write as:

# 1/y dy/dx = 1/x #

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

# ln |y| = ln |x| + lnA #

So that:

# ln |y| = ln A|x| #

# :. y = Ax #