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MATH-WHIZZKID-using-kamke-find-the-genral-solution-for-the-differential-equation-1-x-2-y-x-2-y-2y-0-solve-this-using-forbenius-mtd-1-x-2-y-x-3-3x-y-4-2x-y-0-solve-the-dif

Question Number 210017 by klipto last updated on 28/Jul/24 $$ \\ $$$$\boldsymbol{\mathrm{MATH}}−\boldsymbol{\mathrm{WHIZZKID}} \\ $$$$\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{kamke}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{genral}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}''+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}'−\mathrm{2}\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$−−−−−−−−− \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{forbenius}}\:\boldsymbol{\mathrm{mtd}} \\…

Question-209847

Question Number 209847 by SonGoku last updated on 23/Jul/24 Answered by mr W last updated on 23/Jul/24 $${depth}\:={h} \\ $$$${h}=\sqrt{\mathrm{23}^{\mathrm{2}} −\left(\frac{\mathrm{53}−\mathrm{41}}{\mathrm{2}}\right)^{\mathrm{2}} }=\sqrt{\mathrm{493}}=\mathrm{22}.\mathrm{20}{m} \\ $$$${cross}\:{section}\:{area}\:={A} \\…

Let-u-n-be-a-set-satisfying-u-1-1-amp-u-n-1-u-n-ln-n-u-n-n-1-1-Prove-that-u-2023-gt-2023-ln-2023-2-Find-lim-n-u-n-ln-n-n-

Question Number 209631 by York12 last updated on 17/Jul/24 $$\mathrm{Let}\:{u}_{{n}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{set}\:\mathrm{satisfying}\:{u}_{\mathrm{1}} =\mathrm{1}\:\&\:{u}_{{n}+\mathrm{1}} ={u}_{{n}} +\frac{\mathrm{ln}\:{n}}{{u}_{{n}} }\:\:,\:\forall\:{n}\:\geqslant\mathrm{1} \\ $$$$\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that}\:{u}_{\mathrm{2023}} >\sqrt{\mathrm{2023}.\mathrm{ln}\:\mathrm{2023}}. \\ $$$$\mathrm{2}.\:\mathrm{Find}:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{u}_{{n}} .\mathrm{ln}\:{n}}{{n}}. \\ $$ Terms…