Question

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

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

Answer 1

The correct option is B $e^{-y}=e^{-x}-e^x+c$, c integrating constant

Given differential equation is
$\frac{dy}{dx}=e^{y+x}+e^{y-x}$
$\Rightarrow \int e^{-y}dy=\int (e^x+e^{-x})dx$
$\Rightarrow {-e}^{-y}=e^x-e^{-x}-c$
$\Rightarrow e^{-y}=e^{-x}-e^x+c$