Question

The solution of the equation $\frac{d^{2}y}{d{x}^2}=e^{-2x}$ is:

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

Answer 1

Answer: (B)

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