Q. The 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) $e^{x} - e^{- y} = c$
Explanation
(c)
Given, $\frac{dy}{dx} = e^{x}e^{y}$
$\Rightarrow$ $\int_{}^{}e^{- y}dy = \int_{}^{}e^{x}dx$
$\Rightarrow$ ${- e}^{- y} = e^{x} - c$
$\Rightarrow$ $e^{x} + e^{- y} = c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.