Solve the following differential equations: `(x+y)(dx-dy)=dx+dy`

Explanation

To solve the differential equation \((x+y)(dx-dy)=dx+dy\), we will follow a systematic approach.

### Step-by-Step Solution:

1. **Rewrite the Equation:**
Start with the given equation:
\[
(x+y)(dx-dy) = dx + dy
...