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Category: Differential Equation

Question-128646

Question Number 128646 by Algoritm last updated on 09/Jan/21 Answered by Olaf last updated on 09/Jan/21 $${y}''−\frac{\mathrm{1}+{x}}{{x}}{y}'+\frac{{y}}{{x}}\:=\:\mathrm{0}\:\left(\mathrm{1}\right) \\ $$$${y}''−{y}'−\frac{{y}'−{y}}{{x}}\:=\:\mathrm{0}\:\left(\mathrm{2}\right) \\ $$$$\mathrm{Let}\:{u}\:=\:{y}'−{y}\:\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)\::\:{u}'−\frac{{u}}{{x}}\:=\:\mathrm{0} \\ $$$$\frac{{u}'}{{u}}\:=\:\frac{\mathrm{1}}{{x}}…

Solution-of-differential-eq-dy-dx-y-x-y-ln-y-x-x-ln-x-y-is-

Question Number 128536 by liberty last updated on 08/Jan/21 $$\mathrm{Solution}\:\mathrm{of}\:\mathrm{differential}\:\mathrm{eq}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{y}\left(\mathrm{x}−\mathrm{y}\:\mathrm{ln}\:\mathrm{y}\right)}{\mathrm{x}\left(\mathrm{x}\:\mathrm{ln}\:\mathrm{x}−\mathrm{y}\right)}\:. \\ $$$$\mathrm{is}\:\_ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

3x-2-1-yy-3xy-2-cos-x-e-sin-x-

Question Number 128432 by bemath last updated on 07/Jan/21 $$\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{1}\right)\mathrm{yy}'\:+\mathrm{3xy}^{\mathrm{2}} =\mathrm{cos}\:\mathrm{x}.\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} \: \\ $$ Answered by liberty last updated on 07/Jan/21 $$\mathrm{let}\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{v}\left(\mathrm{x}\right)\Rightarrow\mathrm{2yy}'=\frac{\mathrm{dv}}{\mathrm{dx}} \\…

y-2y-sin-x-2y-3-2-sin-x-

Question Number 128420 by bramlexs22 last updated on 07/Jan/21 $$\:\mathrm{y}'=\mathrm{2y}\:\mathrm{sin}\:\mathrm{x}\:−\mathrm{2y}^{\mathrm{3}/\mathrm{2}} \:\mathrm{sin}\:\mathrm{x}\: \\ $$ Answered by liberty last updated on 07/Jan/21 $$\mathrm{y}'=\mathrm{2sin}\:\mathrm{x}\left(\mathrm{y}−\mathrm{y}^{\mathrm{3}/\mathrm{2}} \right) \\ $$$$\frac{\mathrm{dy}}{\mathrm{y}−\mathrm{y}^{\mathrm{3}/\mathrm{2}} }\:=\:\mathrm{2sin}\:\mathrm{x}\:\mathrm{dx}\:…

dy-dx-x-y-ln-x-y-

Question Number 128395 by bramlexs22 last updated on 06/Jan/21 $$\:\:\:\frac{{dy}}{{dx}}\:=\:\left(\frac{{x}}{{y}}\right)\:\mathrm{ln}\:\left(\frac{{x}}{{y}}\right) \\ $$ Answered by mr W last updated on 07/Jan/21 $${let}\:{x}={yu} \\ $$$$\frac{{dx}}{{dy}}={u}+{y}\frac{{du}}{{dy}} \\ $$$$\mathrm{1}=\left({u}+{y}\frac{{du}}{{dy}}\right){u}\mathrm{ln}\:{u}…

yy-b-x-a-ay-2-1-x-2-

Question Number 128106 by bemath last updated on 04/Jan/21 $$\:\mathrm{yy}'\:+\:\mathrm{b}\left(\mathrm{x}−\mathrm{a}\right)=\:\frac{\mathrm{ay}^{\mathrm{2}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\: \\ $$ Commented by mr W last updated on 05/Jan/21 $${once}\:{i}\:{asked}\:{this}\:{question}\:{due}\:{to} \\ $$$${Q}\mathrm{127997},\:{but}\:{then}\:{i}\:{could}\:{solve}\:{it}\:{myself}…