A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
Correct Answer: B
Solution :
\[y=a\cos (\log x)-b\sin (\log x)\] On differentiating w.r.t.\[x,\] we get \[\frac{dy}{dx}=a\frac{[-\sin (\log x)]}{x}-\frac{b\cos (\log x)}{x}\] \[=-\frac{[a\sin (\log x)+b\cos (\log x)]}{x}\] \[\Rightarrow \] \[x\frac{dy}{dx}=-[a\sin (\log x)+b\cos (\log x)]\] Again, on differentiating w.r.t.\[x,\] we get \[x\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}=-\left[ \frac{a\cos (\log x)}{x}-\frac{b\sin (\log x)}{x} \right]=-\frac{y}{x}\]\[\Rightarrow \] \[{{x}^{2}}\frac{{{d}^{2}}y}{d{{x}^{2}}}+x\frac{dy}{dx}+y=0\]
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