Question

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

• A. $y=\frac{1}{4}{e}^{-2x}+\frac{cx}{2}+d$
• B. $y=\frac{1}{4}{e}^{-2x}+cx+d$
• C. $y=\frac{1}{4}{e}^{-2x}+c{x}^2+d$
• D. $y=\frac{1}{4}{e}^{-2x}+c{x}^3+d$

Answer 1

Answer: (B)

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