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Category: Differential Equation

y-y-e-2x-sin-e-x-

Question Number 131086 by EDWIN88 last updated on 01/Feb/21 $$\:{y}''−{y}\:=\:{e}^{−\mathrm{2}{x}} \:\mathrm{sin}\:\left({e}^{−{x}} \right)\: \\ $$ Answered by liberty last updated on 01/Feb/21 $$\left[\:\mathrm{D}^{\mathrm{2}} −\mathrm{1}\:\right]\mathrm{y}\:=\:\mathrm{e}^{−\mathrm{2x}} \mathrm{sin}\:\left(\mathrm{e}^{−\mathrm{x}} \right)…

y-2xy-

Question Number 143878 by akmalovna05 last updated on 19/Jun/21 $$\mathrm{y}'''=\mathrm{2xy}'' \\ $$ Answered by Ar Brandon last updated on 19/Jun/21 $$\mathrm{y}'''=\mathrm{2xy}''\Rightarrow\frac{\mathrm{y}'''}{\mathrm{y}''}=\mathrm{2x}\Rightarrow\mathrm{ln}\left(\mathrm{y}''\right)=\mathrm{x}^{\mathrm{2}} \Rightarrow\mathrm{y}''=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \\ $$…

x-y-y-x-3-

Question Number 143775 by akmalovna05 last updated on 18/Jun/21 $$\mathrm{x}×\mathrm{y}''−\mathrm{y}=\hat {\mathrm{x}3} \\ $$ Answered by TheHoneyCat last updated on 21/Jun/21 $$\mathrm{I}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{solution}: \\ $$$${f}:\begin{cases}{\mathbb{R}}&{\rightarrow}&{\mathbb{R}}\\{{x}}&{ }&{−{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}}…

x-2dx-

Question Number 143765 by akmalovna05 last updated on 18/Jun/21 $$\int\int{x}+\mathrm{2}{dx} \\ $$ Answered by ajfour last updated on 18/Jun/21 $$\int\left\{\int\left({x}+\mathrm{2}\right){dx}\right\}{dx} \\ $$$$\:=\:\int\:\frac{\left[\left({x}+\mathrm{2}\right)^{\mathrm{2}} +{k}\right]{dx}}{\mathrm{2}} \\ $$$$\:=\frac{\left({x}+\mathrm{2}\right)^{\mathrm{3}}…