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The general solution of the differential equation \( \frac{dy}{dx} = e^{x+y} \)is \[ \begin{array} (A)\: e^x+e^{-y}=C \quad & (B)\: e^x+e^y=C \\ (C)\: e^{-x}+e^y=C \quad & (D)\: e^{-x}+e^{-y}=C \end{array} \]

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