Show that the given differential equation is homogeneous and solve each of them. `(x – y) dy – (x + y) dx = 0`

Explanation

To solve the differential equation \((x - y) dy - (x + y) dx = 0\), we will first show that it is homogeneous and then find its general solution.

### Step 1: Check if the equation is homogeneous
A differential equation is homogeneous if it can be expressed in the form \(M(x, y)dx + N(x, y)dy = 0\) where both \(M\) and \(N\) are homogeneous functions of the same degree.

Here, we can rewrite the given equation:
\[
(x - y) dy = (x + y) dx
...