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Category: Differential Equation

y-y-x-2-1-y-2-

Question Number 103776 by bemath last updated on 17/Jul/20 $${y}'\:−\:\frac{{y}}{{x}^{\mathrm{2}} −\mathrm{1}}\:=\:{y}^{\mathrm{2}} \\ $$ Answered by bemath last updated on 17/Jul/20 $${set}\:{v}\:=\:{y}^{−\mathrm{1}} \:\Rightarrow\frac{{dv}}{{dx}}\:=\:−{y}^{−\mathrm{2}} \:\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}\:=\:−{y}^{\mathrm{2}}…

2y-y-y-cos-3x-

Question Number 103769 by bemath last updated on 17/Jul/20 $$\mathrm{2}{y}''−{y}'+{y}\:=\:\mathrm{cos}\:\mathrm{3}{x} \\ $$ Answered by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{let}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{laplace}\:\mathrm{transform} \\ $$$$\mathrm{e}\:\Rightarrow\mathrm{2L}\left(\mathrm{y}^{''} \right)−\mathrm{L}\left(\mathrm{y}^{'}…

solve-y-y-y-4-at-y-0-1-

Question Number 103767 by bramlex last updated on 17/Jul/20 $${solve}\:{y}'−{y}\:=\:{y}^{\mathrm{4}} \:{at}\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1}\: \\ $$ Answered by bemath last updated on 17/Jul/20 $${substitute}\:{v}\:=\:{y}^{−\mathrm{3}} \\ $$$$\frac{{dv}}{{dx}}\:=\:−\mathrm{3}{y}^{−\mathrm{4}} \:\frac{{dy}}{{dx}}\:\Rightarrow\frac{{dy}}{{dx}}\:=\:−\frac{{y}^{\mathrm{4}} }{\mathrm{3}}\:\frac{{dv}}{{dx}}…

Question-103664

Question Number 103664 by byaw last updated on 16/Jul/20 Answered by bramlex last updated on 16/Jul/20 $$\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}\:=\:\mathrm{2xy}\:\mathrm{dy}\: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2xy}}\:;\:\mathrm{set}\:\mathrm{y}\:=\:\mathrm{zx}\: \\ $$$$\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{z}\:+\:\mathrm{x}\:\frac{\mathrm{dz}}{\mathrm{dx}}…