Solve the differential equation: `(dy)/(dx)+1=e^(x+y)`

Explanation

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

### Step 1: Substitute \(t = x + y\)
Let \(t = x + y\). Then, differentiating both sides with respect to \(x\) gives:
\[ \frac{dt}{dx} = 1 + \frac{dy}{dx} \]
This implies:
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