Question Number 78878 by M±th+et£s last updated on 21/Jan/20 $${x}^{\mathrm{3}} \:{y}'''\:−\:\mathrm{3}{x}^{\mathrm{2}} {y}''+\mathrm{6}{xy}'\:−\mathrm{6}{y}={x}^{\mathrm{4}} \:{ln}\left({x}\right),{x}>\mathrm{0} \\ $$ Answered by mind is power last updated on 21/Jan/20 $${y}={x}^{{a}}…
Question Number 13316 by 433 last updated on 18/May/17 $$\begin{cases}{{x}'\left({t}\right)=\mathrm{4}{x}\left({t}\right)+\mathrm{5}{y}\left({t}\right)}\\{{y}'\left({t}\right)=\mathrm{4}{y}\left({t}\right)}\end{cases} \\ $$ Answered by ajfour last updated on 18/May/17 $${dy}=\mathrm{4}{ydt}\:\:\:\:\: \\ $$$$\int\frac{{dy}}{{y}}=\mathrm{4}\int{dt} \\ $$$$\mathrm{ln}\:\left(\frac{{y}}{{y}_{\mathrm{0}} }\right)=\mathrm{4}{t}\:\:\:\:{or}\:\:\boldsymbol{{y}}=\boldsymbol{{y}}_{\mathrm{0}}…
Question Number 144356 by Ar Brandon last updated on 24/Jun/21 $$\mathrm{y}'+\mathrm{cos}\left(\mathrm{x}\right)\mathrm{y}=\mathrm{cos}^{\mathrm{2}} \mathrm{x} \\ $$ Answered by Olaf_Thorendsen last updated on 24/Jun/21 $${y}'+\mathrm{cos}\left({x}\right){y}\:=\:\mathrm{cos}^{\mathrm{2}} {x}\:\:\:\left(\mathrm{1}\right) \\ $$$${y}\:=\:{e}^{−\mathrm{sin}{x}}…
Question Number 13025 by ARJUN SUBBA last updated on 11/May/17 Commented by prakash jain last updated on 13/May/17 $$\mathrm{A}\:\mathrm{should}\:\mathrm{be}\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by prakash jain…
Question Number 131488 by Ahmed1hamouda last updated on 05/Feb/21 Answered by Ñï= last updated on 18/Feb/21 $${y}''+\mathrm{2}{y}'+\mathrm{5}{y}=\mathrm{6}{e}^{\mathrm{2}{x}} +{xsin}^{\mathrm{2}} {x}+{e}^{{x}} {cos}\mathrm{2}{x} \\ $$$${y}_{{p}} =\frac{\mathrm{1}}{{D}^{\mathrm{2}} +\mathrm{2}{D}+\mathrm{5}}\left(\mathrm{6}{e}^{\mathrm{2}{x}} +{xsin}^{\mathrm{2}}…
Question Number 131466 by Ahmed1hamouda last updated on 05/Feb/21 Commented by Ahmed1hamouda last updated on 05/Feb/21 $$ \\ $$$$\left.\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{n}\right)\mathrm{D} \\ $$ Answered by EDWIN88 last…
Question Number 131452 by Engr_Jidda last updated on 04/Feb/21 $${integrate} \\ $$$$\int_{\mathrm{0}} ^{{n}\pi} \varrho^{\left(\frac{\mathrm{8}{u}}{{n}\pi}\right)} \left(\mathrm{1}−{cos}\mathrm{2}{u}\right){du} \\ $$ Answered by bramlexs22 last updated on 04/Feb/21 $${hint}\::\:{let}\:\frac{\mathrm{8}{u}}{{n}\pi}\:=\:{t}\:\Rightarrow\:\mathrm{2}{u}=\frac{{tn}\pi}{\mathrm{4}}\:;\:{du}\:=\:\frac{{n}\pi}{\mathrm{8}}\:{dt}…
Question Number 131453 by Engr_Jidda last updated on 04/Feb/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by bramlexs22 last updated on 04/Feb/21 $$\:\sqrt{\mathrm{16}−{x}^{\mathrm{2}} }\:=\:{l}\:\Rightarrow\:{x}^{\mathrm{2}} =\mathrm{16}−{l}^{\mathrm{2}} \:;\:{x}\:{dx}\:=\:−{l}\:{dl}…
Question Number 65858 by ugwu Kingsley last updated on 05/Aug/19 Commented by mathmax by abdo last updated on 05/Aug/19 $${x}+\mathrm{2}{y}^{'} \:+{y}\:=\left({x}+\mathrm{2}\right)^{\mathrm{3}} \:\Rightarrow\mathrm{2}{y}^{'} \:+{y}\:=\left({x}+\mathrm{2}\right)^{\mathrm{3}} −{x}\:\Rightarrow \\…
Question Number 324 by 123456 last updated on 25/Jan/15 $${u}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{u}}{\partial{x}}+\frac{\partial{u}}{\partial{y}}=\frac{\left({x}+{y}\right){u}}{{xy}} \\ $$ Answered by prakash jain last updated on 21/Dec/14 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{symmetric}\:\mathrm{in}\:{x},{y}. \\…