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Author: Tinku Tara

Question-138702

Question Number 138702 by peter frank last updated on 16/Apr/21 Answered by mr W last updated on 17/Apr/21 $${y}=\mathrm{sinh}\:{x}+{k}\:\mathrm{cosh}\:{x} \\ $$$$\:\:=\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}\:\left(\frac{\mathrm{1}}{\:\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}}\mathrm{sinh}\:{x}+\frac{{k}}{\:\sqrt{{k}^{\mathrm{2}} −\mathrm{1}}}\:\mathrm{cosh}\:{x}\right) \\…

By-the-use-of-substitution-x-2-show-that-the-legendary-equation-1-2-y-2-y-n-n-1-y-0-where-n-is-a-constant-change-to-hyper-geometric-equation-hence-obtain-the-solution-to-

Question Number 7628 by Tawakalitu. last updated on 06/Sep/16 $${By}\:{the}\:{use}\:{of}\:{substitution}\:\:{x}\:=\:\mu^{\mathrm{2}} ,\:{show}\:{that} \\ $$$${the}\:{legendary}\:{equation}\:, \\ $$$$\left(\mathrm{1}\:−\:\mu^{\mathrm{2}} \right){y}''\:−\:\mathrm{2}\mu{y}'\:+\:{n}\left({n}\:+\:\mathrm{1}\right){y}\:=\:\mathrm{0},\: \\ $$$${where}\:{n}\:{is}\:{a}\:{constant}\:{change}\:{to}\:{hyper}\:{geometric} \\ $$$${equation}\:.\:{hence}\:{obtain}\:{the}\:{solution}\:{to}\:{the}\: \\ $$$${resulting}\:{hyper}\:{geometric}\:{differential}\:{equation}\: \\ $$$${by}\:{way}\:{of}\:{comparison}. \\…