Question

The differential equation of $y=A{e}^{2x}+B{e}^{-2x}$ is :

• A. $\frac{dy}{dx}-4y=0$
• B. $\frac{d^{2}y}{d{x}^2}-4y=0$
• C. $\frac{d^{2}y}{d{x}^2}=y^2$
• D. $\frac{d^{2}y}{d{x}^2}-y=0$

Answer 1

Answer: (B)

Given : $y=A{e}^{2x}+B{e}^{-2x}$
$\therefore \frac{dy}{dx}=A{e}^{2x}.2+B{e}^{-2x}\left(-2\right)$
$\Rightarrow \frac{dy}{dx}=2A{e}^{2x}-2B{e}^{-2x}$
$\frac{d^{2}y}{d{x}^2}=2A{e}^{2x}.2-2B{e}^{-2x}(-2)$
$=4A{e}^{2x}+4B{e}^{-2x}$
$\Rightarrow \frac{d^{2}y}{d{x}^2}=4y\Rightarrow \frac{d^{2}y}{d{x}^2}-4y=0$