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