Question Number 207106 by Wuji last updated on 07/May/24 $${Calculate}\:{the}\:{generalized}\:{solution}\:{for}\:{the}\:{following} \\ $$$${system}\:{of}\:{ODEs}: \\ $$$$\frac{{dx}}{{dt}}=−\frac{\mathrm{1}}{\mathrm{2}}{x},\:\frac{{dy}}{{dt}}=\frac{\mathrm{1}}{\mathrm{2}}{x}−\frac{\mathrm{1}}{\mathrm{4}}{y},\:\:\frac{{dz}}{{dt}}=\frac{\mathrm{1}}{\mathrm{4}}{y}−\frac{\mathrm{1}}{\mathrm{6}}{z} \\ $$ Answered by mr W last updated on 07/May/24 $$\begin{vmatrix}{−\frac{\mathrm{1}}{\mathrm{2}}−\lambda}&{\mathrm{0}}&{\mathrm{0}}\\{\frac{\mathrm{1}}{\mathrm{2}}}&{−\frac{\mathrm{1}}{\mathrm{4}}−\lambda}&{\mathrm{0}}\\{\mathrm{0}}&{\frac{\mathrm{1}}{\mathrm{4}}}&{−\frac{\mathrm{1}}{\mathrm{6}}−\lambda}\end{vmatrix}=\mathrm{0}…
Question Number 206976 by mokys last updated on 02/May/24 $$\:{find}\:{the}\:{sum}\:{of}\::\:\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:{e}^{−\mathrm{2}\lambda_{{i}} \:{t}} \\ $$ Commented by mr W last updated on 02/May/24 $${what}\:{are}\:{the}\:\lambda_{{i}} \:?…
Question Number 206861 by MrGHK last updated on 28/Apr/24 $$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\boldsymbol{\mathrm{k}}^{\mathrm{2}} }\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}+\boldsymbol{\mathrm{n}}} }\left(\frac{\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{k}}+\mathrm{1}\right)\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{k}}+\mathrm{1}} }{\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{k}}+\mathrm{2}\right)}\right)=??? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 206837 by akolade last updated on 27/Apr/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 206838 by akolade last updated on 27/Apr/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 206781 by yogei last updated on 25/Apr/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 206794 by MaruMaru last updated on 25/Apr/24 $${help}\:{me}… \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left({t}\right)\mathrm{ln}\left({t}\right)}{{t}}{e}^{−{t}} \:{dt} \\ $$ Answered by Berbere last updated on 25/Apr/24 $${let}\:{f}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 206788 by SANOGO last updated on 25/Apr/24 Answered by A5T last updated on 25/Apr/24 $$\mathrm{1}.\:\overline {\left(\frac{{x}}{{y}}\right)}=\frac{\overset{−} {{x}}}{\overset{−} {{y}}}\Rightarrow\overset{} {\left(\frac{\mathrm{1}}{{z}}\right)}=\frac{\overset{−} {\mathrm{1}}}{\overset{−} {{z}}}=\frac{\mathrm{1}}{\overset{−} {{z}}} \\…
Question Number 206764 by mustafazaheen last updated on 24/Apr/24 Answered by A5T last updated on 24/Apr/24 $${f}\left({g}\left(−\mathrm{3}\right)\right)={f}\left(\sqrt{−\mathrm{3}}\right)={f}\left(\sqrt{\mathrm{3}}{i}\right)=\left(\sqrt{\mathrm{3}}{i}\right)^{\mathrm{2}} =−\mathrm{3} \\ $$ Commented by JDamian last updated…
Question Number 206746 by sonukgindia last updated on 23/Apr/24 Answered by A5T last updated on 23/Apr/24 $${f}\left(\mathrm{2}\right)+\mathrm{2}{f}\left(−\mathrm{1}\right)=\mathrm{2}…\left({i}\right) \\ $$$${f}\left(−\mathrm{1}\right)+\mathrm{2}{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=−\mathrm{1}…\left({ii}\right) \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\mathrm{2}{f}\left(\mathrm{2}\right)=\frac{\mathrm{1}}{\mathrm{2}}…\left({iii}\right) \\ $$$$\mathrm{2}×\left({iii}\right)−\left({ii}\right):\:\mathrm{4}{f}\left(\mathrm{2}\right)−{f}\left(−\mathrm{1}\right)=\mathrm{2}…\left({iv}\right) \\ $$$$\mathrm{2}×\left({iv}\right)+\left({i}\right):\:\mathrm{9}{f}\left(\mathrm{2}\right)=\mathrm{6}\Rightarrow{f}\left(\mathrm{2}\right)=\frac{\mathrm{2}}{\mathrm{3}}…