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Author: Tinku Tara

Pls-i-need-a-help-from-Ordinary-differantial-Equation-t-2-y-2-t-t-y-1-t-t-2-2-y-t-0-we-Already-Know-Solution-y-t-C-1-J-t-C-2-J-t-But-J-t-can-t-Satisfy-as-Solutio

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Question Number 212906 by issac last updated on 26/Oct/24 $$\mathrm{Pls}\:\mathrm{i}\:\mathrm{need}\:\mathrm{a}\:\mathrm{help}.. \\ $$$$\mathrm{from}\:\mathrm{Ordinary}\:\mathrm{differantial}\:\mathrm{Equation} \\ $$$${t}^{\mathrm{2}} {y}^{\left(\mathrm{2}\right)} \left({t}\right)+{t}\centerdot{y}^{\left(\mathrm{1}\right)} \left({t}\right)+\left({t}^{\mathrm{2}} −\nu^{\mathrm{2}} \right){y}\left({t}\right)=\mathrm{0} \\ $$$$\mathrm{we}\:\mathrm{Already}\:\mathrm{Know} \\ $$$$\mathrm{Solution}\:{y}\left({t}\right)={C}_{\mathrm{1}} {J}_{\nu} \left({t}\right)+{C}_{\mathrm{2}}…

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dx-x-5-1-

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Question Number 212896 by MrGaster last updated on 26/Oct/24 $$\int\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}} \\ $$ Commented by Frix last updated on 26/Oct/24 $${x}^{\mathrm{5}} −\mathrm{1}=\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right) \\…

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Question-212899

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Question Number 212899 by vasil92 last updated on 26/Oct/24 Answered by MrGaster last updated on 02/Nov/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{{n}} }{dx}=\mathrm{1} \\ $$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[{x}−\frac{{x}^{{n}−\mathrm{1}} }{\left({n}+\mathrm{1}\right)\centerdot^{\mathrm{2}}…

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