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Question Number 6511 by Yozzii last updated on 30/Jun/16
$${Find}\:{the}\:{function}\:{y}\:{satisfying} \\ $$$${y}'+\frac{{c}_{\mathrm{1}} }{{y}\left({x}−{c}_{\mathrm{2}} \right)^{{n}} }={c}_{\mathrm{3}} \\ $$$${where}\:{n}\in\left(\mathbb{Z}−\left\{\mathrm{0}\right\}\right),\:{c}_{\mathrm{1}} \:{and}\:{c}_{\mathrm{3}} \:{are}\:{nonzero} \\ $$$${constants},\:{and}\:{c}_{\mathrm{2}} \:{is}\:{constant}. \\ $$