Question Number 46858 by maxmathsup by imad last updated on 01/Nov/18 $${solve}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:−\frac{\mathrm{2}{x}}{{x}^{\mathrm{3}} \:+\mathrm{1}}{y}^{'} \:\:+{xy}\:={x}\:{e}^{−\mathrm{2}{x}} . \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 46857 by maxmathsup by imad last updated on 01/Nov/18 $${solve}\:\mathrm{2}{x}\:{y}^{'} \:+\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}\:={xe}^{−{x}} \:\:\:{withy}\left({o}\right)=\mathrm{1}\: \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 112358 by john santu last updated on 07/Sep/20 $${The}\:{point}\:{of}\:{the}\:{curve}\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{2}} =\mathrm{72} \\ $$$${which}\:{nearest}\:{to}\:{the}\:{line}\:\mathrm{3}{x}+\mathrm{2}{y}=\mathrm{1} \\ $$$${is\_\_\_} \\ $$$$\left({a}\right)\:\left(\mathrm{6},\mathrm{3}\right)\:\:\:\:\:\:\:\left({c}\right)\:\left(\mathrm{6},\mathrm{6}\right) \\ $$$$\left({b}\right)\:\left(\mathrm{6},−\mathrm{3}\right)\:\:\left({d}\right)\:\left(\mathrm{6},\mathrm{5}\right) \\ $$ Answered by…
Question Number 46640 by canhtoan last updated on 29/Oct/18 $$\mathrm{1}\leqslant{n},{m}\in\mathbb{N}.\:{Prove}\:{that} \\ $$$$\mathrm{3}\left({m}+{n}\right)+\mathrm{10ln}\:\left({m}!{n}!\right)\geqslant\mathrm{6}\sqrt{{mnH}_{{m}} {H}_{{n}} }. \\ $$$$\left({H}_{{m}} =\underset{{i}=\mathrm{1}} {\overset{{m}} {\sum}}\frac{\mathrm{1}}{{i}},\:{H}_{{n}} =\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{j}}\right) \\ $$ Commented…
Question Number 46609 by maxmathsup by imad last updated on 29/Oct/18 $${solve}\:\:\:\:{x}\:{y}^{''} \:−{e}^{−{x}} {y}^{'} \:\:\:={x}\:{sinx} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 46608 by maxmathsup by imad last updated on 29/Oct/18 $${let}\:{the}\:{d}.{e}\:\:{xy}^{''} \:+\left({x}^{\mathrm{2}} −{x}\right){y}^{'} \:+\mathrm{2}{y}\:=\mathrm{0} \\ $$$${find}\:{a}\:{solution}\:{developpable}\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 112114 by mnjuly1970 last updated on 06/Sep/20 $$\:\:{solution}\:{of} \\ $$$$\Phi=\int_{\mathrm{0}} ^{\mathrm{1}} {xH}_{{x}} {dx}\:\overset{\gamma+\psi\left({x}+\mathrm{1}\right)} {=}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\left(\gamma+\psi\left({x}+\mathrm{1}\right)\right){dx}\: \\ $$$$\:\overset{\psi\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{x}}+\psi\left({x}\right)} {=}\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\left(\gamma+\frac{\mathrm{1}}{{x}}+\psi\left({x}\right)\right){dx} \\ $$$$=\frac{\gamma}{\mathrm{2}}+\mathrm{1}+\:\int_{\mathrm{0}}…
Question Number 111965 by mnjuly1970 last updated on 05/Sep/20 $$\:\:\:\:\:\:….{advanced}\:\:{calculus}… \\ $$$${evaluate}: \\ $$$$ \\ $$$$\:\:\:\:{i}::\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {xH}_{{x}} {dx}\:=???\:\: \\ $$$$\:\:\:\:\:{ii}::\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{\mathrm{2}} \mathrm{2}^{{n}\:}…
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Question Number 177456 by cortano1 last updated on 05/Oct/22 Answered by a.lgnaoui last updated on 05/Oct/22 $${posons}\:\:{x}=\mathrm{sin}\:{t}\:\:\:\:{alors}\:{y}=\mathrm{cos}\:{t} \\ $$$$\frac{\mathrm{1}}{\mathrm{sin}\:{t}}+\frac{\mathrm{4}}{\mathrm{cos}\:{t}}=\frac{\mathrm{cos}\:{t}+\mathrm{4sin}\:{t}}{\mathrm{sin}\:{t}\mathrm{cos}\:{t}} \\ $$$$\left.{le}\:{rapoort}\:\:{est}\:{minimale}\:\:{si}\:\:\:\mathrm{scos}\:{t}+\mathrm{4sin}\:{t}\:{mnimale}\right) \\ $$$$\begin{cases}{\mathrm{cos}\:{t}+\mathrm{4sin}\:{t}=\mathrm{0}}\\{\mathrm{sin}\:{t}\mathrm{cos}\:{t}\neq\mathrm{0}}\end{cases} \\ $$$$\mathrm{4sin}\:{t}=−\mathrm{cos}\:{t}\:\:\:\mathrm{tan}\:{t}=−\frac{\mathrm{1}}{\mathrm{4}}=\frac{\mathrm{sin}\:{t}}{\mathrm{cos}\:{t}}…