Question Number 105118 by john santu last updated on 26/Jul/20 $${x}^{\mathrm{2}} {y}''+{xy}'−{y}\:=\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\: \\ $$ Answered by john santu last updated on 26/Jul/20 $$\Rightarrow\:{x}^{\mathrm{2}} {y}''+\mathrm{2}{xy}'−{xy}'\:−\:{y}\:=\:\frac{\mathrm{1}}{{x}+\mathrm{1}} \\…
Question Number 104893 by bramlex last updated on 24/Jul/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{tan}\:{x}\:\frac{{dy}}{{dx}}\:=\:\mathrm{sec}\:{x}\:+\:\mathrm{cot}\:{x} \\ $$ Answered by mathmax by abdo last updated on 24/Jul/20 $$\mathrm{y}^{''} \:+\mathrm{tanx}\:\mathrm{y}^{'}…
Question Number 170410 by Mastermind last updated on 23/May/22 $${Given}\:{y}={xe}^{−{x}} ,\:{show}\:{that} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{2}\frac{{dy}}{{dx}}+{y}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by floor(10²Eta[1]) last…
Question Number 104845 by john santu last updated on 24/Jul/20 $${solve}\:{y}'\:=\:{y}−{x}−\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$ Answered by john santu last updated on 24/Jul/20 $$\frac{{dy}}{{dx}}\:=\:−\left({x}−{y}+\mathrm{2}\right)+\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$$${set}\:{x}−{y}+\mathrm{2}\:=\:{m}\: \\…
Question Number 170329 by ali009 last updated on 21/May/22 $${find}\:{the}\:{general}\:{solution}\:{of}\: \\ $$$$\left.\mathrm{1}\right){y}'''−\mathrm{7}{y}'+\mathrm{6}{y}={x} \\ $$$$\left.\mathrm{2}\right){y}'''−\mathrm{3}{y}''+\mathrm{2}{y}'=\frac{{e}^{{x}} }{\mathrm{1}+{e}^{−{x}} } \\ $$ Answered by LEKOUMA last updated on 22/May/22…
Question Number 104669 by bramlex last updated on 23/Jul/20 $$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\:{dy}\:=\:{xy}\:{dx}\: \\ $$ Answered by bemath last updated on 23/Jul/20 $${set}\:{y}\:=\:{zx}\: \\ $$$$\frac{{dy}}{{dx}}\:=\:{z}\:+\:{x}\:\frac{{dz}}{{dx}} \\…
Question Number 104659 by bobhans last updated on 23/Jul/20 $${what}\:{is}\:{remainder}\:{of}\:\mathrm{12}!\:{in}\:{mod}\:\mathrm{17} \\ $$ Answered by bramlex last updated on 23/Jul/20 $${we}\:{can}\:{use}\:{Wilson}'{s}\:{theorem} \\ $$$${by}\:{which}\:\mathrm{16}!\:\equiv\:−\mathrm{1}\:\left({mod}\:\mathrm{17}\right) \\ $$$${Now}\:{use}\:{that}\: \\…
Question Number 104651 by Ar Brandon last updated on 23/Jul/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{2t}\right). \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Complementary}\:\mathrm{Function}\:\mathrm{is}; \\ $$$$\mathrm{y}_{\mathrm{CF}} =\mathrm{acos}\left(\mathrm{t}\right)+\mathrm{bsin}\left(\mathrm{t}\right), \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{form}\:\mathrm{can}\:\mathrm{the}\:\mathrm{particular}\:\mathrm{integral}\:\mathrm{be}\:\mathrm{expressed} \\ $$$$\mathrm{so}\:\mathrm{as}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{given}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}?…
Question Number 104599 by Ar Brandon last updated on 22/Jul/20 $$\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right)\mathrm{x}'\left(\mathrm{t}\right)+\mathrm{t}^{\mathrm{2}} \mathrm{x}\left(\mathrm{t}\right)+\mathrm{2}\left(\mathrm{x}\left(\mathrm{t}\right)\right)^{\mathrm{2}} =\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104595 by Ar Brandon last updated on 22/Jul/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathcal{DE} \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{2x}'\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{te}^{−\mathrm{t}} \\ $$ Answered by mathmax by abdo last updated on 22/Jul/20 $$\left.\mathrm{h}\right)\rightarrow\mathrm{r}^{\mathrm{2}}…