Q. The solution of the differential equation $\frac{dy}{dx} = e^{x - y} + x^{2}e^{- y}$ is
A) $y = e^{x - y} - x^{2}e^{- y} + c$
B) $e^{y} - e^{x} = \frac{1}{3}\ x^{3} + c$
C) $e^{x} + e^{y} = \frac{1}{3}\ x^{3} + c$
D) $e^{x} - e^{y} = \frac{1}{3}\ x^{3} + c$
Explanation
(b)
Given, $\frac{dy}{dx} = e^{- y}(e^{x} + x^{2})$
$\Rightarrow$ $\int_{}^{}e^{y}dy = \int_{}^{}e^{x}dx + \int_{}^{}x^{2}dx$
$\Rightarrow$ $e^{y} = e^{x} + \frac{x^{3}}{3} + c$
$\Rightarrow$ $e^{y} - e^{x} = \frac{x^{3}}{3} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.