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 $$\frac{{dy}}{{dx}}−\mathrm{csc}\:\mathrm{2}{x}.{y}\:=\:\mathrm{csc}\:\mathrm{2}{x}.\mathrm{tan}\:{x} \\ $$$${integrating}\:{factor}\: \\ $$$${u}\left({x}\right)=\:{e}^{\int\:\mathrm{csc}\:\mathrm{2}{x}\:{dx}} \:=\:{e}^{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mid\mathrm{tan}\:{x}\mid}…
Question Number 171336 by cortano1 last updated on 13/Jun/22 Answered by mr W last updated on 13/Jun/22 $${k}=\frac{{y}}{{x}} \\ $$$${x}^{\mathrm{2}} −\mathrm{10}{x}+{k}^{\mathrm{2}} {x}^{\mathrm{2}} −\mathrm{10}{kx}+\mathrm{41}=\mathrm{0} \\ $$$$\left(\mathrm{1}+{k}^{\mathrm{2}}…
Question Number 105738 by bobhans last updated on 31/Jul/20 $$\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} \\ $$$$\frac{{dy}}{{dx}}\:=\:\vartheta\:+\:{x}\:\frac{{d}\vartheta}{{dx}}…
Question Number 105734 by bemath last updated on 31/Jul/20 $$\left(\mathrm{2}{x}+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\mathrm{cot}\:{x}\right)\:{dx}\:+\mathrm{2}{y}\:{dy}\:=\:\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 105710 by john santu last updated on 31/Jul/20 $$\left(\mathrm{2}{xy}+\mathrm{cos}\:{y}\right)\:{dx}\:+\left({x}^{\mathrm{2}} −{x}\mathrm{sin}{y}−\mathrm{2}{y}\right){dy}=\mathrm{0} \\ $$ Answered by Smail last updated on 31/Jul/20 $${let}\:{M}=\mathrm{2}{xy}+{cosy}\:{and}\:\:{N}={x}^{\mathrm{2}} −{xsiny}−\mathrm{2}{y} \\ $$$$\frac{{dM}}{{dy}}=\mathrm{2}{x}−{siny}…
Question Number 105659 by bemath last updated on 30/Jul/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}−\mathrm{2}{y}=\mathrm{2}{x}\: \\ $$ Answered by john santu last updated on 30/Jul/20 Commented by bramlex…
Question Number 105646 by Ar Brandon last updated on 30/Jul/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 105638 by bemath last updated on 30/Jul/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{9}{y}\:=\:\mathrm{cos}\:\mathrm{4}{x} \\ $$ Answered by bramlex last updated on 30/Jul/20 $${HE}\::\:\flat^{\mathrm{2}} +\mathrm{9}\:=\:\mathrm{0}\:;\:\flat=\pm\mathrm{3}{i} \\ $$$${y}_{{h}}…
Question Number 105632 by Ar Brandon last updated on 30/Jul/20 $$\mathrm{Given}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} }{\mathrm{n}!}\mathrm{e}^{\mathrm{x}} \mathrm{dx}\:,\:\mathrm{n}\in\mathbb{N} \\ $$$$\mathrm{a}\backslash\mathrm{Show}\:\mathrm{that}\:\forall\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right],\:\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{n}} \mathrm{e}^{\mathrm{x}} \leqslant\mathrm{e}\:\mathrm{and}\:\mathrm{deduce}\:\mathrm{that}\:\mathrm{the}\: \\ $$$$\mathrm{Sequence}\:\left(\mathrm{I}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{converges}\:\mathrm{to}\:\mathrm{zero}. \\…
Question Number 105603 by bemath last updated on 30/Jul/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{4}\frac{{dy}}{{dx}}+{y}\:=\:{a}\:\mathrm{sin}\:\mathrm{2}{x} \\ $$ Answered by bobhans last updated on 30/Jul/20 $$\mathcal{H}{omogenous}\:{equation} \\ $$$$\nu^{\mathrm{2}} −\mathrm{4}\nu+\mathrm{1}=\mathrm{0}\:\rightarrow\nu=\frac{\mathrm{4}\pm\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{2}}…