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

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

Using the exponential property $e^{x+y} = e^x \cdot e^y$:

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

Dividing both sides by $e^y$:

$\frac{1}{e^y} \cdot \frac{dy}{dx} = e^x$

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

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

Integrating both sides:

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

$-e^{-y} = e^x + C_1$

Multiplying both sides by $-1$:

$e^{-y} = -e^x - C_1$

$e^x + e^{-y} = -C_1$

Since $-C_1$ is an arbitrary constant, it can be written as $C$:

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

Therefore, the general solution is $e^x + e^{-y} = C$