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suppose-y-x-n-0-a-n-x-n-statisfies-y-y-y-2-e-y-1with-y-0-0-and-y-0-1-determin-a-4-

Question Number 218891 by Nicholas666 last updated on 17/Apr/25 $$ \\ $$$$\:\boldsymbol{{suppose}}\:\boldsymbol{{y}}\left(\boldsymbol{{x}}\right)\:=\:\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\boldsymbol{{a}}_{\boldsymbol{{n}}} \boldsymbol{{x}}^{\boldsymbol{{n}}} \boldsymbol{{statisfies}}\: \\ $$$$\:\:\:\boldsymbol{{y}}''\boldsymbol{{y}}−\left(\boldsymbol{{y}}'\right)^{\mathrm{2}} =\boldsymbol{{e}}^{\boldsymbol{{y}}} −\mathrm{1}\boldsymbol{{with}}\:\boldsymbol{{y}}\left(\mathrm{0}\right)=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{y}}'\left(\mathrm{0}\right)=\mathrm{1}.\:\:\:\:\: \\ $$$$\:\:\:\:\boldsymbol{{determin}}\:\boldsymbol{{a}}_{\mathrm{4}} . \\ $$$$…

Question-218658

Question Number 218658 by Nicholas666 last updated on 14/Apr/25 Answered by Nicholas666 last updated on 14/Apr/25 Commented by A5T last updated on 14/Apr/25 $$\mathrm{x}\leqslant\mathrm{3}\:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{1}\:\mathrm{does}\:\mathrm{not}\:\mathrm{imply}\:\mathrm{xy}\leqslant\mathrm{3} \\…

Question-218399

Question Number 218399 by Nicholas666 last updated on 09/Apr/25 Answered by MrGaster last updated on 10/Apr/25 $$\begin{array}{|c|}{{f}\left({n}\right)=\frac{{n}^{\mathrm{2}} }{\mathrm{2}}}\\\hline\end{array}\mathrm{when}\:{n}\:\mathrm{is}\:\mathrm{even} \\ $$$$\cancel{{f}\left({n}\right)=\frac{{n}^{\mathrm{2}} }{\mathrm{2}}} \\ $$$${f}\left({n}\right)=\frac{{n}^{\mathrm{2}} −\tau\left({n}\right)}{\mathrm{2}} \\…