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Author: Tinku Tara

let-b-i-a-i-gt-0-where-i-1-2-3-n-amp-i-1-n-b-i-Prove-that-b-1-b-2-b-1-b-2-a-1-a-2-b-1-b-3-b-1-b-3-a-1-a-3-b-2-b-3-b-2-b-3-

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Question Number 196870 by York12 last updated on 02/Sep/23 $${let}\:{b}_{{i}} \wedge\:{a}_{{i}} >\mathrm{0}\:{where}\:{i}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},…,{n}\right\}\&\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left({b}_{{i}} \right)=\lambda\:{Prove}\:{that} \\ $$$$\frac{\lambda−\left({b}_{\mathrm{1}} +{b}_{\mathrm{2}} \right)}{\left({b}_{\mathrm{1}} +{b}_{\mathrm{2}} \right)}\left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} \right)+\frac{\lambda−\left({b}_{\mathrm{1}} +{b}_{\mathrm{3}} \right)}{\left({b}_{\mathrm{1}}…

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Question-196852

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Question Number 196852 by SANOGO last updated on 01/Sep/23 Answered by Mathspace last updated on 02/Sep/23 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}^{{b}} }{dt}\:=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{{a}−\mathrm{1}} \sum_{{n}=\mathrm{0}} ^{\infty}…

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Question-196848

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Question Number 196848 by sonukgindia last updated on 01/Sep/23 Commented by Frix last updated on 01/Sep/23 $$\mathrm{The}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{42}\:\left(\mathrm{or}\:\mathrm{else}\:\mathrm{prove}\:\mathrm{it}'\mathrm{s}\:\boldsymbol{{not}}\:\mathrm{42}\right) \\ $$ Answered by AST last updated on…

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2xy-1-4x-y-2x-1-y-y-

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Question Number 196846 by mokys last updated on 01/Sep/23 $$\mathrm{2}{xy}''\:+\:\left(\mathrm{1}−\mathrm{4}{x}\right){y}'\:+\:\left(\mathrm{2}{x}−\mathrm{1}\right){y}\:=\:{y} \\ $$ Answered by witcher3 last updated on 04/Sep/23 $$\mathrm{2xy}''+\left(\mathrm{1}−\mathrm{4x}\right)\mathrm{y}'+\left(\mathrm{2x}−\mathrm{1}\right)\mathrm{y}=\mathrm{0} \\ $$$$\mathrm{y}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}} ..\mathrm{solution} \\ $$$$\mathrm{y}=\mathrm{ze}^{\mathrm{x}}…

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