If y=ax+x2+1n+bx-x2+1-n, prove that x2+1d2ydx2+xdydx-n2y=0.Disclaimer: – InterviewSolution

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1.	If y=ax+x2+1n+bx-x2+1-n, prove that x2+1d2ydx2+xdydx-n2y=0.Disclaimer: There is a misprint in the question, x2+1d2ydx2+xdydx-n2y=0 must be written instead of x2-1d2ydx2+xdydx-n2y=0.
Answer» $If y = a {\{x + \sqrt{x^{2} + 1}\}}^{n} + b {\{x - \sqrt{x^{2} + 1}\}}^{- n}, prove that (x^{2} + 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} - n^{2} y = 0 .$ Disclaimer: There is a misprint in the question, $(x^{2} + 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} - n^{2} y = 0$ must be written instead of $(x^{2} - 1) \frac{d^{2} y}{d x^{2}} + x \frac{d y}{d x} - n^{2} y = 0 .$

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