Solve the following differential equations: `(x+y+1)(dy)/(dx)=1`

Explanation

To solve the differential equation \((x+y+1) \frac{dy}{dx} = 1\), we will follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ (x + y + 1) \frac{dy}{dx} = 1 \]
We can rewrite this as:
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