Question

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

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

Answer 1

The Correct Option is A

The correct answer is A:$e^x+e^{-y}=C$
$\frac{dy}{dx}=e^{x+y}=e^x.e^y$
$⇒\frac{dy}{e^y}=e^xdx$
$⇒e^{-y} dy=e^x dx$
Integrating both sides,we get:
$∫e^{-y} dy=∫e^x dx$
$⇒-e^{-y}=e^x+k$
$⇒e^x+e^{-y}=-k$
$⇒e^x+e^{-y}=c\,\,\, (c=-k)$
Hence,the correct answer is A.