A) \[{{n}^{2}}y\]
B) \[-y\]
C) \[-{{n}^{2}}y\]
D) None of these
Correct Answer: C
Solution :
\[y=A\cos (nx)+B\sin (nx)\] \[\therefore dy/dx=-nA\sin (nx)+nB\cos (nx)\] Again \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-{{n}^{2}}A\cos (nx)-{{n}^{2}}B\sin (nx)\] \[=-{{n}^{2}}[A\cos (nx)+B\sin (nx)]\] Þ \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-{{n}^{2}}y\].
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