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