Question

The solution of the equation $ \frac{d^{2}y}{dx^{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}+cx^{2}+d $
• D. $ y=\frac{1}{4}\,e^{-2x}+cx^{3}+d $

Answer 1

Answer: (B)

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