A) \[\frac{dy}{dx}+8y=0\]
B) \[\frac{dy}{dx}-8y=0\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y=0\]
D) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}-9y=0\]
Correct Answer: C
Solution :
Let\[y=4\sin 3x\Rightarrow \frac{dy}{dx}=12\cos 3x\] Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-36\sin 3x=-9\times 4\sin 3x=-9y\] Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y=0\].
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