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Category: Differential Equation

Question-105877

Question Number 105877 by john santu last updated on 01/Aug/20 Answered by bemath last updated on 01/Aug/20 $$\frac{{dy}}{{dx}}.\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}+{y}^{\mathrm{2}} }{{y}^{\mathrm{4}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\:=\:\mathrm{0} \\ $$$$\frac{{y}^{\mathrm{4}} \:{dy}}{\mathrm{1}+{y}^{\mathrm{2}}…

sin-2x-dy-dx-y-tan-x-

Question Number 105854 by bobhans last updated on 01/Aug/20 $$\mathrm{sin}\:\mathrm{2}{x}\:\frac{{dy}}{{dx}}\:−{y}\:=\:\mathrm{tan}\:{x} \\ $$ Answered by bemath last updated on 01/Aug/20 $$\frac{{dy}}{{dx}}−\mathrm{csc}\:\mathrm{2}{x}.{y}\:=\:\mathrm{csc}\:\mathrm{2}{x}.\mathrm{tan}\:{x} \\ $$$${integrating}\:{factor}\: \\ $$$${u}\left({x}\right)=\:{e}^{\int\:\mathrm{csc}\:\mathrm{2}{x}\:{dx}} \:=\:{e}^{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{tan}\:{x}\mid}…

x-tan-y-x-y-sec-2-y-x-dx-x-sec-2-y-x-dy-0-

Question Number 105738 by bobhans last updated on 31/Jul/20 $$\left({x}\:\mathrm{tan}\:\left(\frac{{y}}{{x}}\right)−{y}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right)\right)\:{dx}−{x}\:\mathrm{sec}\:^{\mathrm{2}} \left(\frac{{y}}{{x}}\right){dy}=\mathrm{0} \\ $$ Answered by john santu last updated on 01/Aug/20 $${set}\:\frac{{y}}{{x}}\:=\:\vartheta\:\Rightarrow{y}=\vartheta{x} \\ $$$$\frac{{dy}}{{dx}}\:=\:\vartheta\:+\:{x}\:\frac{{d}\vartheta}{{dx}}…