Verify that $y = 4 s i n 3 x$ is the solution of the differential equation $\frac{d^{2} y}{d x^{2}} + 9 y = 0$ .

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Solution

$\begin{matrix} y = 4 sin 3 x \frac{d y}{d x} = 12 cos 3 x \frac{d^{2} y}{d x^{2}} = - 36 sin 3 x = - 9 x (4 sin 3 x) \frac{d^{2} y}{d x^{2}} = - 9 y \frac{d^{2} y}{d x^{2}} + 9 y = 0 \end{matrix}$

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$y = 4 s i n 3 x$ is a solution of the differential equation

[AI CBSE 1986]

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