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