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Question Number 36696 by kumar12513 last updated on 04/Jun/18
if y=tan^(−1) x show that  (1+x^2 )y_(n+2) +2(n+1)xy_(n+1) +n(n+1)y_n =0
$${if}\:{y}={tan}^{−\mathrm{1}} {x}\:{show}\:{that} \\ $$$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} +\mathrm{2}\left({n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +{n}\left({n}+\mathrm{1}\right){y}_{{n}} =\mathrm{0} \\ $$

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