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Category: Differential Equation

xdx-ydy-xdy-ydx-

Question Number 148466 by Ar Brandon last updated on 28/Jul/21 $$\mathrm{xdx}+\mathrm{ydy}=\mathrm{xdy}−\mathrm{ydx} \\ $$ Answered by bramlexs22 last updated on 28/Jul/21 $$\left({x}+{y}\right){dx}=\left({x}−{y}\right){dy} \\ $$$$\:\frac{{dy}}{{dx}}=\:\frac{{x}+{y}}{{x}−{y}} \\ $$$$\:{let}\:{y}={ux}\:\Rightarrow\frac{{dy}}{{dx}}\:=\:{u}\:+\:{x}\:\frac{{du}}{{dx}}…

e-2-x-x-y-x-dx-dy-1-x-0-

Question Number 82883 by jagoll last updated on 26/Feb/20 $$\left[\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\:\sqrt{\mathrm{x}}}−\frac{\mathrm{y}}{\:\sqrt{\mathrm{x}}}\:\right]\:.\frac{\mathrm{dx}}{\mathrm{dy}}\:=\:\mathrm{1}\:,\:\mathrm{x}\:\neq\:\mathrm{0} \\ $$ Answered by john santu last updated on 26/Feb/20 $$\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\:\sqrt{\mathrm{x}}}\:−\:\frac{\mathrm{y}}{\:\sqrt{\mathrm{x}}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\right)\:\mathrm{y}\:=\:\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}}…

Solve-dy-dx-2cos-2x-3-2y-with-y-0-1-i-for-what-value-of-x-gt-0-does-the-situation-exist-ii-for-what-value-of-x-is-y-x-maximum-

Question Number 17323 by tawa tawa last updated on 04/Jul/17 $$\mathrm{Solve}:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2cos}\left(\mathrm{2x}\right)}{\mathrm{3}\:−\:\mathrm{2y}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{with}\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)\:=\:−\mathrm{1} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:>\:\mathrm{0}\:\mathrm{does}\:\mathrm{the}\:\mathrm{situation}\:\mathrm{exist} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{is}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{maximum} \\ $$ Answered by Tinkutara last updated on 04/Jul/17 $$\left(\mathrm{3}\:−\:\mathrm{2}{y}\right)\:{dy}\:=\:\mathrm{2}\:\mathrm{cos}\:\mathrm{2}{x}\:{dx}…

2×2-9x-10-

Question Number 16918 by rustylee last updated on 28/Jun/17 $$\mathrm{2}{x}\mathrm{2}+\mathrm{9}{x}=\mathrm{10} \\ $$ Answered by Joel577 last updated on 28/Jun/17 $$\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{9}{x}\:−\:\mathrm{10}\:=\:\mathrm{0} \\ $$$${x}_{\mathrm{1},\mathrm{2}} \:=\:\frac{−\mathrm{9}\:\pm\:\sqrt{\mathrm{81}\:+\:\mathrm{80}}}{\mathrm{4}} \\…

how-to-minimalize-t-x-2-x-1-1-y-x-2-x-2-y-x-2-c-1-c-0-x-t-

Question Number 147762 by DomaPeti last updated on 23/Jul/21 $${how}\:{to}\:{minimalize}\:{t}? \\ $$$$\underset{{x}_{\mathrm{2}} } {\overset{{x}_{\mathrm{1}} } {\int}}\frac{\sqrt{\mathrm{1}+\left({y}\left({x}\right)'\right)^{\mathrm{2}} }}{\:\sqrt{{x}^{\mathrm{2}} +{y}\left({x}\right)^{\mathrm{2}} }\centerdot{c}_{\mathrm{1}} +{c}_{\mathrm{0}} }\Delta{x}={t} \\ $$$$ \\ $$…