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Category: Differential Equation

dy-dx-2x-y-1-x-4y-3-

Question Number 169558 by greougoury555 last updated on 03/May/22 $$\:\:\:\:\:\:\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{2}{x}−{y}+\mathrm{1}}{{x}−\mathrm{4}{y}+\mathrm{3}}\:\:\: \\ $$ Answered by ali009 last updated on 03/May/22 $${a}\mathrm{1}=\mathrm{2}\:\:{a}\mathrm{2}=\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\mathrm{1}/{a}\mathrm{2}=\mathrm{2} \\ $$$${b}\mathrm{1}=−\mathrm{1}\:\:{b}\mathrm{2}=−\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:{b}\mathrm{1}/{b}\mathrm{2}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${so} \\…

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}^{'}…