Question

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

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

Answer 1

Answer: (B)

$\because \frac{d^{2} y}{d x^{2}}=e^{-2 x}$
$\Rightarrow \frac{d y}{d x}=\frac{e^{\cdot 2 x}}{-2}+c$
$\Rightarrow y=\frac{e^{2 x}}{4}+c x+d$