If y=xna coslogx+b sinlogx, prove that x2d2ydx2+1-2nxdydx+1+n2y=0.Disc – InterviewSolution

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1.	If y=xna coslogx+b sinlogx, prove that x2d2ydx2+1-2nxdydx+1+n2y=0.Disclaimer: There is a misprint in the question. It must be x2d2ydx2+1-2nxdydx+1+n2y=0 instead of x2d2ydx2+1-2ndydx+1+n2y=0.
Answer» $If y = x^{n} \{a \cos (\log x) + b \sin (\log x)\}, prove that x^{2} \frac{d^{2} y}{d x^{2}} + (1 - 2 n) x \frac{d y}{d x} + (1 + n^{2}) y = 0 .$ Disclaimer: There is a misprint in the question. It must be $x^{2} \frac{d^{2} y}{d x^{2}} + (1 - 2 n) x \frac{d y}{d x} + (1 + n^{2}) y = 0$ instead of $x^{2} \frac{d^{2} y}{d x^{2}} + (1 - 2 n) \frac{d y}{d x} + (1 + n^{2}) y = 0$ .

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