Question

The solution of the differential equation $\frac{d^{2}y}{d{x}^2}=e^{-2x},$ where $c$ and $d$ are constants of integration, is

• A. $y=\frac{e^{-2x}}{4}$
• B. $y=\frac{e^{-2x}}{4}+cx+d$
• C. $y=\frac{1}{4}{e}^{-2x}+c{x}^2+d$
• D. $y=\frac{1}{4}{e}^{-4x}+cx+d$

Answer 1

The correct option is B $y=\frac{e^{-2x}}{4}+cx+d$

$\frac{d^{2}y}{d{x}^2}=e^{-2x}$
On integrating both sides, we get
$\Rightarrow \frac{dy}{dx}=\frac{e^{-2x}}{-2}+c$
Again integrating both sides, we get
$\Rightarrow y=\frac{e^{-2x}}{4}+cx+d$