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Category: Differential Equation

dy-dx-y-xy-5-

Question Number 129126 by benjo_mathlover last updated on 13/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}\:=\:\mathrm{xy}^{\mathrm{5}} \: \\ $$ Answered by liberty last updated on 13/Jan/21 $$\:\mathrm{let}\:\mathrm{v}\:=\:\mathrm{y}^{−\mathrm{4}} \:;\:\frac{\mathrm{dv}}{\mathrm{dx}}\:=−\mathrm{4y}^{−\mathrm{5}\:} \frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:−\frac{\mathrm{1}}{\mathrm{4}}\mathrm{y}^{\mathrm{5}}…

solve-the-following-equation-xtan-y-x-ysec-2-y-x-dx-xsec-2-y-x-dy-0-

Question Number 128971 by Ahmed1hamouda last updated on 11/Jan/21 $${solve}\:{the}\:{following}\:{equation} \\ $$$$\left({x}\mathrm{tan}\left(\frac{{y}}{{x}}\right)−{y}\mathrm{sec}^{\mathrm{2}} \left(\frac{{y}}{{x}}\right)\right){dx}−{x}\mathrm{sec}^{\mathrm{2}} \left(\frac{{y}}{{x}}\right){dy}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

x-3-y-3-dx-3xy-2-dy-

Question Number 128689 by bemath last updated on 09/Jan/21 $$\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} \right)\:\mathrm{dx}\:=\:\mathrm{3xy}^{\mathrm{2}} \:\mathrm{dy}\: \\ $$ Answered by liberty last updated on 09/Jan/21 $$\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\mathrm{3xy}^{\mathrm{2}}…

Question-128667

Question Number 128667 by sarahvalencia last updated on 09/Jan/21 Commented by liberty last updated on 09/Jan/21 $$\:\left(\mathrm{1}\right)\:\mathrm{a}^{\mathrm{2}} \mathrm{da}\:+\:\mathrm{2ab}\:\mathrm{db}\:+\:\mathrm{b}^{\mathrm{2}} \:\mathrm{da}\:=\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{d}\left(\mathrm{ab}^{\mathrm{2}} \right)\:+\:\mathrm{a}^{\mathrm{2}} \:\mathrm{da}\:=\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\int\:\mathrm{d}\left(\mathrm{ab}^{\mathrm{2}}…

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}} \\…