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} \\ $$$$\nu^{\mathrm{2}} −\mathrm{4}\nu+\mathrm{1}=\mathrm{0}\:\rightarrow\nu=\frac{\mathrm{4}\pm\mathrm{2}\sqrt{\mathrm{3}}}{\mathrm{2}}…
Question Number 105569 by bemath last updated on 30/Jul/20 $${x}^{\mathrm{2}} \:\frac{{dy}}{{dx}}\:−\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} \:=\:\mathrm{0}\: \\ $$ Answered by john santu last updated on 30/Jul/20 $$\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{3}{xy}+\mathrm{2}{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }…
Question Number 105564 by Ar Brandon last updated on 30/Jul/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{y}''+\mathrm{4y}'+\mathrm{5y}=\mathrm{xe}^{−\mathrm{2x}} \mathrm{sinx} \\ $$ Answered by bobhans last updated on 30/Jul/20 $${Homogenous}\:{equation} \\…
Question Number 170998 by 2407 last updated on 06/Jun/22 Answered by ali009 last updated on 06/Jun/22 $${r}^{\mathrm{2}} +\mathrm{3}{r}+\mathrm{2}=\mathrm{0} \\ $$$${r}=−\mathrm{1}\:\:\:\:{r}=−\mathrm{2} \\ $$$${y}_{{h}} ={C}_{\mathrm{1}} {e}^{−{x}} ×{C}_{\mathrm{2}}…
Question Number 105361 by bemath last updated on 28/Jul/20 $${solve}\:{by}\:{Frobenius}\:{method} \\ $$$${x}^{\mathrm{2}} {y}''−{x}\left(\mathrm{2}{x}−\mathrm{1}\right){y}'+\left({x}+\mathrm{1}\right){y}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 170847 by cortano1 last updated on 01/Jun/22 Commented by ali009 last updated on 01/Jun/22 $${i}\:{think}\:{it}'{s}\:\frac{{dx}}{{dy}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 105283 by bemath last updated on 27/Jul/20 $$\left(\mathrm{1}\right)\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}{xy}}{\mathrm{4}{x}^{\mathrm{2}} −{y}^{\mathrm{3}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{{y}\left(\mathrm{2ln}\:{y}\:+\:\mathrm{1}\right)} \\ $$ Answered by bobhans last updated on 27/Jul/20 $$\left(\mathrm{2}\right)\:{y}\left(\mathrm{2ln}\:{y}+\mathrm{1}\right)\:{dy}\:=\:\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)\:{dx} \\…