Q. If $\frac{dy}{dx} + y = 2e^{2x}$, then $y$ is equal to
A) $ce^{x} + \frac{2}{3}e^{2x}$
B) $(1 - x)e^{- x} + \frac{2}{3}\ e^{2x} + c$
C) $ce^{- x} + \frac{2}{3}\ e^{2x}$
D) $e^{- x} + \frac{2}{3}\ e^{2x} + c$
Explanation
(c)
Given, $\frac{dy}{dx} + y = 2e^{2x}$
$\therefore$ $IF = e^{\int_{}^{}{1\ dx}} = e^{x}$
$\therefore$ Required solution is
$ye^{x} = 2\int_{}^{}e^{2x}e^{x}dx = \frac{2}{3}e^{3x} + c$
$\Rightarrow$ $y = \frac{2}{3}e^{2x} + ce^{- x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.