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Category: Differential Equation

Calculate-the-quadruple-integralas-follows-I-0-1-0-x-0-y-0-z-sin-x-2-y-2-z-2-w-2-1-w-2-z-2-dw-dz-dy-dx-

Question Number 211703 by MrGaster last updated on 17/Sep/24 $$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}}…

certificate-I-0-2-x-2-ln-2-cos-x-lncos-x-dx-2-2ln2-

Question Number 211560 by MrGaster last updated on 13/Sep/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \sqrt{\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \boldsymbol{\mathrm{cos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{\mathrm{lncos}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}\sqrt{\mathrm{2}\boldsymbol{\mathrm{ln}}\mathrm{2}} \\ $$$$ \\ $$ Terms of Service…

dx-x-2-4x-13-

Question Number 211546 by MrGaster last updated on 12/Sep/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\boldsymbol{{dx}}}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{13}}}=? \\ $$ Answered by Frix last updated on 12/Sep/24 $$\int\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{13}}}\:\overset{\left[{t}=\frac{{x}−\mathrm{2}+\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{13}}}{\mathrm{3}}\right]}…

Question-210786

Question Number 210786 by zhou0429 last updated on 19/Aug/24 Answered by Berbere last updated on 19/Aug/24 $${x}^{\mathrm{9}} +\mathrm{1}=\underset{{k}=\mathrm{0}} {\overset{\mathrm{8}} {\prod}}\left({x}−{e}^{{i}\pi\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{9}}\right)} \right)={p}\left({x}\right) \\ $$$$=\Sigma\int\frac{\mathrm{1}}{\left({x}−{e}^{{i}\pi\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{9}}\right)} \right){p}'\left({e}^{{i}\pi\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{9}}\right)} \right)}{dx}…

help-me-to-solve-this-please-y-1-y-2-x-2-solve-this-differential-equation-

Question Number 208569 by pticantor last updated on 18/Jun/24 $$\boldsymbol{{help}}\:\boldsymbol{{me}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{please}} \\ $$$$\:\:\boldsymbol{{y}}''−\sqrt{\mathrm{1}+\boldsymbol{{y}}'^{\mathrm{2}} }=\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{{solve}}\:\boldsymbol{{this}}\:\boldsymbol{{differential}}\:\boldsymbol{{equation}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Terms of…

y-W-

Question Number 207991 by efronzo1 last updated on 02/Jun/24 $$\:\:\:\:\:\mathrm{y}\:\underline{\underbrace{\mathcal{W}}} \\ $$ Answered by mr W last updated on 02/Jun/24 $${particular}\:{solution}: \\ $$$${y}={A}\:\mathrm{sin}\:{x}+{B}\:\mathrm{cos}\:{x} \\ $$$${y}'={A}\:\mathrm{cos}\:{x}−{B}\:\mathrm{sin}\:{x}…