if-y-sin-msin-1-x-prove-that-1-x-2-y-n-2-2n-1-xy-n-1-m-2-n-2-y-n-0-

Question Number 90679 by MWSuSon last updated on 25/Apr/20

$${if}\:{y}={sin}\left({m}\mathrm{sin}^{−\mathrm{1}} {x}\right),\:{prove}\:{that}\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} −\left(\mathrm{2}{n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +\left({m}^{\mathrm{2}} −{n}^{\mathrm{2}} \right){y}_{{n}} =\mathrm{0} \\ $$

Commented by MWSuSon last updated on 25/Apr/20

$${using}\:{Leibnitz}\:{method}\:{please}. \\ $$

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