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Category: Differential Equation

x-dy-dx-y-cos-2y-x-3x-4-

Question Number 89978 by jagoll last updated on 20/Apr/20 $$\left(\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}\right)\left(\mathrm{cos}\:\left(\frac{\mathrm{2y}}{\mathrm{x}}\right)\right)\:=\:−\mathrm{3x}^{\mathrm{4}} \\ $$ Commented by john santu last updated on 20/Apr/20 $$\left[\:{let}\:{y}\:=\:{ux}\:\right]\:\Rightarrow\frac{{dy}}{{dx}}\:=\:{u}\:+\:{x}\frac{{du}}{{dx}} \\ $$$$\left\{{ux}\:+{x}^{\mathrm{2}} \:\frac{{du}}{{dx}}\:−{ux}\:\right\}\left(\mathrm{cos}\:\mathrm{2}{u}\right)\:=\:−\mathrm{3}{x}^{\mathrm{4}} \\…

Solve-the-differential-equstion-d-2-y-dx-2-y-0-2y-1-y-2-h-2-

Question Number 89908 by I want to learn more last updated on 19/Apr/20 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equstion}: \\ $$$$\:\:\:\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:\:\:=\:\:\:\frac{\mathrm{y}_{\mathrm{0}} \:\:−\:\:\mathrm{2y}_{−\mathrm{1}} \:\:+\:\:\mathrm{y}_{−\mathrm{2}} }{\mathrm{h}^{\mathrm{2}} } \\ $$ Commented…