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Category: Differential Equation

solve-x-dy-dx-y-x-

Question Number 224 by 123456 last updated on 25/Jan/15 $$\mathrm{solve} \\ $$$${x}\frac{{dy}}{{dx}}+{y}=\alpha{x}+\beta \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\frac{{dy}}{{dx}}+\frac{{y}}{{x}}=\frac{\alpha{x}+\beta}{{x}} \\ $$$$\mathrm{Integrating}\:\mathrm{Factor}={e}^{\int\frac{\mathrm{1}}{{x}}{dx}} ={e}^{\mathrm{ln}\:{x}}…

solve-the-differential-equation-e-y-1-cos-x-dx-e-y-sin-x-dy-0-

Question Number 182 by sudhanshur last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left({e}^{{y}} +\mathrm{1}\right)\mathrm{cos}\:{x}\:{dx}+{e}^{{y}} \mathrm{sin}\:{x}\:{dy}=\mathrm{0} \\ $$ Answered by 123456 last updated on 14/Dec/14 $$\mathrm{we}\:\mathrm{have}\:\left({e}^{{y}} +\mathrm{1}\right)\mathrm{cos}\:{x}\:{dx}+{e}^{{y}}…

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 $$\mathrm{y}'''=\mathrm{2xy}''\Rightarrow\frac{\mathrm{y}'''}{\mathrm{y}''}=\mathrm{2x}\Rightarrow\mathrm{ln}\left(\mathrm{y}''\right)=\mathrm{x}^{\mathrm{2}} \Rightarrow\mathrm{y}''=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \\ $$…