Question

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

Answer 1

`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`