Q. The solution of the equation $\frac{d^{2}y}{dx^{2}} = e^{- 2x}$ is
A) $\frac{e^{- 2x}}{4}$
B) $\frac{e^{- 2x}}{4} + cx + d$
C) $\frac{1}{4}\ e^{- 2x} + cx^{2} + d$
D) $\frac{1}{4}\ e^{- 2x} + c + d$
Explanation
(b)
Given, $\frac{d^{2}y}{dx^{2}} = e^{- 2x}$
$\Rightarrow$ $\frac{dy}{dx} = \frac{e^{- 2x}}{- 2} + c$ [integrating]
$\Rightarrow$ $y = \frac{e^{- 2x}}{4} + cx + d$ [integrating]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.