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