The general solution of the differential equation `(dy)/(dx)=e^(x+y)`is(A) `e^x+e^(-y)=C` (B) `e^x+e^y=C`(C) `e^(-x)+e^y=C` (D) `e^(-x)+e^(-y)=C`

Explanation

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

### Step 1: Rewrite the equation
We start with the given equation:
\[ \frac{dy}{dx} = e^{x+y} \]
We can rewrite \(e^{x+y}\) as \(e^x \cdot e^y\). Thus, we have:
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