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 :
\[y=4\sin 3x\] ?(i) \[\Rightarrow \] \[\frac{dy}{dx}=12\cos 3x\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-36\sin 3x\] \[\Rightarrow \] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+9y=0\] [from (i)]
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