Question Number 182139 by Mastermind last updated on 04/Dec/22 $$\mathrm{Find}\:\mathrm{constant}\:\mathrm{a},\:\mathrm{b},\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{y}\left(\mathrm{t}\right)=\left(\mathrm{t}+\mathrm{3}\right)\mathrm{e}^{\mathrm{2t}} \:\mathrm{is}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{IVP} \\ $$$$\mathrm{y}^{'} =\mathrm{ay}+\mathrm{e}^{\mathrm{2t}} ,\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{b} \\ $$$$ \\ $$$$. \\ $$ Commented by…
Question Number 182069 by Mastermind last updated on 03/Dec/22 $$\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{3xy}=\mathrm{5x} \\ $$$$ \\ $$$$\mathrm{solve} \\ $$ Commented by CElcedricjunior last updated on 04/Dec/22 $$\left(\mathrm{1}+\boldsymbol{{x}}^{\mathrm{2}}…
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Question Number 116480 by Dwaipayan Shikari last updated on 04/Oct/20 $$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+…….. \\ $$ Answered by Olaf last updated on 04/Oct/20 $${u}_{{n}} \:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} +\mathrm{7}{n}}\:=\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{7}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{7}}\left(\frac{\mathrm{1}}{{n}}−\frac{\mathrm{1}}{{n}+\mathrm{7}}\right) \\ $$$$\underset{{n}=\mathrm{1}}…
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Question Number 50892 by peter frank last updated on 21/Dec/18 $${solve}\:{the}\:{equation} \\ $$$$\mathrm{tan}\:\mathrm{3}\theta{cot}\theta+\mathrm{1}=\mathrm{0}\:{for} \\ $$$$\mathrm{0}\leqslant\theta\leqslant\mathrm{180} \\ $$$$\left.{b}\right){show}\:{that}\:{if}\:\mathrm{cos}\:\mathrm{2}\theta\:{is}\:{not}\:{zero} \\ $$$${then} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{sec}\:\mathrm{2}\theta=\mathrm{2}\left[\frac{\mathrm{cos}\:^{\mathrm{4}} \theta+\mathrm{sin}\:^{\mathrm{4}} \theta}{\mathrm{cos}\:^{\mathrm{4}} \theta−\mathrm{sin}\:^{\mathrm{4}} \theta}\right]…
Question Number 50835 by Tawa1 last updated on 21/Dec/18 Commented by Tawa1 last updated on 21/Dec/18 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{it}\:\mathrm{with}\:\mathrm{diagram} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 116348 by Dwaipayan Shikari last updated on 03/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\left(\mathrm{5}+\mathrm{x}\right)\left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{2}} }{\mathrm{x}\left(\mathrm{1}+\mathrm{x}\right)}\:\:\left(\mathrm{x}\neq−\mathrm{1},\mathrm{0}\right) \\ $$ Commented by MJS_new last updated on 03/Oct/20 $$−\infty<\frac{\left(\mathrm{5}+{x}\right)\left(\mathrm{2}+{x}\right)^{\mathrm{2}} }{{x}\left(\mathrm{1}+{x}\right)}<\infty \\ $$$$\Rightarrow\:\mathrm{minimum}\:\mathrm{is}\:−\infty…
Question Number 50796 by lihao12345 last updated on 20/Dec/18 $$\int\mathrm{1}/\left(\mathrm{1}+{x}^{\mathrm{4}} \right){dx}= \\ $$ Commented by Abdo msup. last updated on 20/Dec/18 $${this}\:{integral}\:{is}\:{solved}\:\:{i}\:{give}\:{the}\:{key} \\ $$$${we}\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \:+\mathrm{1}}…