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Category: Differential Equation

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}. \\…

Question-7216

Question Number 7216 by peter james last updated on 16/Aug/16 Answered by Yozzia last updated on 16/Aug/16 $${ln}\left({x}+{y}\right)−{ln}\left({x}+\mathrm{3}\right)+{ln}\mid\frac{\mathrm{3}−{y}}{{x}+\mathrm{3}}\mid={B}−{ln}\mid{x}+\mathrm{3}\mid \\ $$$${Let}\:{u}=\frac{{x}+{y}}{{x}+\mathrm{3}}\Rightarrow{y}={u}\left({x}+\mathrm{3}\right)−{x} \\ $$$$\therefore\:{y}'={u}'\left({x}+\mathrm{3}\right)+{u}−\mathrm{1} \\ $$$$\Rightarrow{y}'+\mathrm{1}={u}+{u}'\left({x}+\mathrm{3}\right). \\…

x-1-dy-dx-xy-2xe-x-

Question Number 138240 by bobhans last updated on 11/Apr/21 $$\:\left({x}−\mathrm{1}\right)\frac{{dy}}{{dx}}\:+{xy}\:=\:\mathrm{2}{xe}^{−{x}} \\ $$ Answered by EDWIN88 last updated on 11/Apr/21 $$\:\frac{{dy}}{{dx}}\:+\:\frac{{x}}{{x}−\mathrm{1}}\:{y}\:=\:\frac{\mathrm{2}{x}}{{e}^{{x}} \left({x}−\mathrm{1}\right)} \\ $$$${put}\:{IF}\:=\:{e}^{\int\:\frac{{x}}{{x}−\mathrm{1}}\:{dx}} \:=\:{e}^{\int\:\frac{{x}−\mathrm{1}+\mathrm{1}}{{x}−\mathrm{1}}\:{dx}} ={e}^{{x}+\mathrm{ln}\:\left({x}−\mathrm{1}\right)}…

Solve-this-equation-by-reducing-it-from-non-homogeneous-equation-to-homogeneous-equation-dy-dx-2-x-y-1-3x-y-1-Please-help-with-this-one-too-i-was-trying-your-approah-but-not-the-s

Question Number 6661 by Tawakalitu. last updated on 09/Jul/16 $${Solve}\:{this}\:{equation}\:{by}\:{reducing}\:{it}\:{from}\:{non}\:{homogeneous} \\ $$$${equation}\:{to}\:{homogeneous}\:{equation} \\ $$$$\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}\left({x}\:+\:{y}\:−\:\mathrm{1}\right)}{\mathrm{3}{x}\:+\:{y}\:+\:\mathrm{1}} \\ $$$$ \\ $$$${Please}\:{help}\:{with}\:{this}\:{one}\:{too}. \\ $$$${i}\:{was}\:{trying}\:{your}\:{approah}\:{but}\:{not}\:{the}\:{same} \\ $$$$ \\ $$$${thanks}\:{for}\:{your}\:{help}. \\…

Solve-this-equation-by-reducing-it-from-non-homogeneous-equation-to-homogeneous-equation-dy-dx-x-y-3-x-y-5-

Question Number 6651 by Tawakalitu. last updated on 08/Jul/16 $${Solve}\:{this}\:{equation}\:{by}\:{reducing}\:{it}\:{from}\:{non}\:{homogeneous} \\ $$$${equation}\:{to}\:{homogeneous}\:{equation}\: \\ $$$$\frac{{dy}}{{dx}}\:=\:\frac{{x}\:+\:{y}\:+\:\mathrm{3}}{{x}\:−\:{y}\:−\mathrm{5}} \\ $$ Commented by prakash jain last updated on 09/Jul/16 $$\mathrm{Substitue}\:{x}={u}+\mathrm{1}\:\mathrm{and}\:{y}={v}−\mathrm{4}…