Question

Solution of the differential equation $\frac{dy}{dx}=2e^{x-y}+x^2{e}^{-y}$ is

• A. $e^{-y}=2e^x+\frac{x^3}{3}+c$
• B. $e^y=2e^{-x}+\frac{x^3}{3}+c$
• C. $e^y=2e^x+\frac{x^3}{3}+c$
• D. $e^{-y}=2e^x+\frac{x^{-3}}{3}+c$

Answer 1

The correct option is C $e^y=2e^x+\frac{x^3}{3}+c$

Solution of the differential equation:
$\frac{dy}{dx}=(2e^x+x^2)e^{-y}\Rightarrow e^{y}dy=(2e^x+x^2)dx$
Intregrating both side,
$\Rightarrow \int e^{y}dy=\int (2e^x+x^2)dx+c\Rightarrow e^y=2e^x+\frac{x^3}{3}+c$