Question

$y=4sin3x$ is a solution of the differential equation

[AI CBSE 1986]

• A. $\frac{dy}{dx}+8y=0$
• B. $\frac{dy}{dx}-8y=0$
• C. $\frac{d^{2}y}{d{x}^2}+9y=0$
• D. $\frac{d^{2}y}{d{x}^2}-9y=0$

Answer 1

The correct option is C

$\frac{d^{2}y}{d{x}^2}+9y=0$

Let $y=4sin3x\Rightarrow \frac{dy}{dx}=12cos3x\Rightarrow \frac{d^{2}y}{d{x}^2}=-36sin3x=-9\times 4sin3x=-9y\Rightarrow \frac{d^{2}y}{d{x}^2}+9y=0.$