For the differential equation `x y(dy)/(dx)=(x+2)(y+2)`, find the solution curve passing through the point `(1, -1)`.

Explanation

To solve the differential equation \( x y \frac{dy}{dx} = (x + 2)(y + 2) \) and find the solution curve passing through the point \( (1, -1) \), we can follow these steps:

### Step 1: Separate the Variables
We start with the given equation:
\[ x y \frac{dy}{dx} = (x + 2)(y + 2) \]
We can rearrange this to separate the variables:
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