Question

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 $

Answer 1

Answer: (B)

$ \frac{d^{2}y}{dx^{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 $