Question

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

• A. $e^x+e^{-y}=c$
• B. $e^{-x}+e^y=c$
• C. $e^{-x}+e^{-y}=c$
• D. $e^x+e^y=c$

Answer 1

The correct option is A $e^x+e^{-y}=c$

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

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

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

Integrating both sides, we get

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

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

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

$\text{Taking}-C=c$

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

Hence, Option (A) is correct,