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Category: Differential Equation

bemath-1-d-2-y-dx-2-6-dy-dx-9y-1-x-x-2-2-x-3-3y-3-11-x-2-y-xy-2-6-

Question Number 106775 by bemath last updated on 07/Aug/20 $$\:\:\:\:\:\:\:\:\:\:\:^{@\mathrm{bemath}@} \\ $$$$\:\left(\mathrm{1}\right)\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{6}\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{9y}\:=\:\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} \\ $$$$\:\:\left(\mathrm{2}\right)\:\begin{cases}{\mathrm{x}^{\mathrm{3}} +\mathrm{3y}^{\mathrm{3}} \:=\:\mathrm{11}}\\{\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\mathrm{xy}^{\mathrm{2}} \:=\:\mathrm{6}}\end{cases}\: \\ $$ Answered by abdomathmax…

if-1-u-x2-y2-z2-then-x-u-x-y-u-y-z-u-z-

Question Number 41028 by Choudharyvishal155@gmail.com last updated on 31/Jul/18 $${if}\:\mathrm{1}/{u}\:=\:\sqrt{\left({x}\mathrm{2}\:+\:{y}\mathrm{2}\:+{z}\mathrm{2}\right)} \\ $$$${then}\:{x}\partial{u}/\partial{x}\:+\:{y}\partial{u}/\partial{y}\:+\:{z}\partial{u}/\partial{z}\:=\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 31/Jul/18 $${u}=\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}\:\:{so}\:\:\frac{\partial{u}}{\partial{x}}=\frac{−\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}}…

d-2-x-dt-2-a-b-1-l-x-2-l-2-x-Find-x-t-if-x-0-x-0-x-0-0-

Question Number 40920 by ajfour last updated on 29/Jul/18 $$\frac{{d}^{\:\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }={a}−{b}\left(\mathrm{1}−\frac{{l}}{\:\sqrt{{x}^{\mathrm{2}} +{l}^{\mathrm{2}} }}\right){x}\: \\ $$$${Find}\:{x}\left({t}\right)\:{if}\:{x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} \:,\:{x}'\left(\mathrm{0}\right)=\mathrm{0}\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…

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}…