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: Separate the variables
We can rewrite the equation to separate the variables \(y\) and \(x\):
\[ \frac{dy}{dx} = e^{x+y} \]
This can be rewritten as:
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