The general solution of differential equation $\frac{dy}{dx}= e^{x+y}$ is

$e^x + e^{-y}= C$, where C is an arbitrary constant

The correct answer is Option (2) → $e^x + e^{-y}= C$, where C is an arbitrary constant

Given differential equation

$\frac{dy}{dx}=e^{x+y}$

Separate variables

$e^{-y}dy=e^x dx$

Integrate both sides

$\int e^{-y}dy=\int e^x dx$

$-e^{-y}=e^x+C$

$e^x+e^{-y}=C$

The general solution is $e^x+e^{-y}=C$.