Show that the differential equation `(x-y)(dy)/(dx)=x+2y`is homogeneous and solve it

Explanation

To solve the differential equation \((x - y) \frac{dy}{dx} = x + 2y\), we will first show that it is homogeneous and then solve it.

### Step 1: Show that the differential equation is homogeneous

A differential equation is homogeneous if it can be expressed in the form \(\frac{dy}{dx} = f\left(\frac{y}{x}\right)\).

1. Rearranging the given equation:
\[
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