Solve the differential equation `y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))`.

Explanation

To solve the differential equation \( y - x \frac{dy}{dx} = a \left( y^2 + \frac{dy}{dx} \right) \), we will follow these steps:

### Step 1: Rearranging the Equation
Start by rearranging the given equation to isolate \(\frac{dy}{dx}\):
\[ y - a y^2 = x \frac{dy}{dx} + a \frac{dy}{dx} \]
This simplifies to:
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