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Author: Tinku Tara

if-x-2x-10x-e-2t-at-t-0-x-0-and-x-1-find-x-t-using-laplace-transform-

Question Number 219491 by OmoloyeMichael last updated on 26/Apr/25 $$\boldsymbol{{if}}\:\boldsymbol{{x}}''−\mathrm{2}\boldsymbol{{x}}'+\mathrm{10}\boldsymbol{{x}}=\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{{t}}} ,\:\boldsymbol{{at}}\:\boldsymbol{{t}}=\mathrm{0},\boldsymbol{{x}}=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{x}}'=\mathrm{1} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}}\left(\boldsymbol{{t}}\right)\:\boldsymbol{{using}}\:\boldsymbol{{laplace}}\:\boldsymbol{{transform}} \\ $$ Answered by mahdipoor last updated on 26/Apr/25 $${Laplace}\:\Rightarrow \\ $$$$\left({Xs}^{\mathrm{2}}…

a-b-c-are-the-roots-of-the-equation-x-3-3x-1-0-find-a-1-3-b-1-3-c-1-3-amp-1-a-1-3-1-b-1-3-1-c-1-3-

Question Number 219454 by mr W last updated on 25/Apr/25 $${a},\:{b},\:{c}\:{are}\:{the}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0}. \\ $$$${find}\:\sqrt[{\mathrm{3}}]{{a}}+\sqrt[{\mathrm{3}}]{{b}}+\sqrt[{\mathrm{3}}]{{c}}=?\:\&\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{b}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{c}}}=? \\ $$ Commented by mr W last updated on…

L-sinx-0-e-sx-sinx-dx-0-e-sx-e-ix-e-ix-2i-dx-1-2i-0-e-s-i-x-dx-0-e-s-i-x-dx-1-2i-1-s-i-e-s-i-x-1-s-i-e-s-i-x-0-1-

Question Number 219449 by Lukos last updated on 25/Apr/25 $${L}\left\{{sinx}\right\}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} {sinx}\:{dx}=\int_{\mathrm{0}} ^{\infty} {e}^{−{sx}} \frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}{i}}\left[\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}−{i}\right){x}} {dx}\:\:−\int_{\mathrm{0}} ^{\infty} {e}^{−\left({s}+{i}\right){x}}…

Question-219451

Question Number 219451 by Nicholas666 last updated on 25/Apr/25 Commented by Nicholas666 last updated on 25/Apr/25 $$\mathrm{This}\:\mathrm{is}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{beyond}\:\mathrm{My}\:\mathrm{control},\:\:\: \\ $$$$\:\mathrm{can}\:\mathrm{You}\:\mathrm{solve}\:\mathrm{friends}? \\ $$$$ \\ $$ Terms of…

prove-0-r-2-t-2-e-wt-dt-rpiL-1-rw-rpiI-1-rw-2riK-1-rw-2w-

Question Number 219445 by SdC355 last updated on 25/Apr/25 $${prove} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\sqrt{{r}^{\mathrm{2}} −{t}^{\mathrm{2}} }{e}^{−{wt}} \mathrm{d}{t}=\frac{−{r}\pi\boldsymbol{\mathrm{L}}_{\mathrm{1}} \left({rw}\right)+{r}\pi{I}_{\mathrm{1}} \left({rw}\right)+\mathrm{2}{r}\boldsymbol{{i}}{K}_{\mathrm{1}} \left({rw}\right)}{\mathrm{2}{w}} \\ $$ Commented by MrGaster…