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-

Tinku Tara June 3, 2023 Differential Equation 0 Comments

Question Number 7628 by Tawakalitu. last updated on 06/Sep/16

By the use of substitution x = μ^2 , show that the legendary equation , (1 − μ^2 )y′′ − 2μy′ + n(n + 1)y = 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.

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

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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-

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