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Category: Differential Equation

Solve-y-y-x-0-

Question Number 14288 by tawa tawa last updated on 30/May/17 $$\mathrm{Solve}:\:\:\mathrm{y}'\:+\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{0} \\ $$ Answered by Tinkutara last updated on 30/May/17 $$\frac{{dy}}{{dx}}\:=\:−\:\frac{{y}}{{x}}\: \\ $$$$\frac{{dy}}{{y}}\:=\:−\:\frac{{dx}}{{x}} \\ $$$$\mathrm{ln}\:{y}\:=\:−\:\mathrm{ln}\:{x}\:+\:{C}…

yy-x-e-x-y-

Question Number 145300 by imjagoll last updated on 04/Jul/21 $$\:\:\:\:\:\:\:\mathrm{yy}'\:=\:\mathrm{x}\:\mathrm{e}^{\frac{\mathrm{x}}{\mathrm{y}}} \: \\ $$ Answered by puissant last updated on 04/Jul/21 $$\mathrm{y}'=\frac{\mathrm{x}}{\mathrm{y}}\mathrm{e}^{\frac{\mathrm{x}}{\mathrm{y}}} \:\:\mathrm{put}\:\:\:\mathrm{t}=\frac{\mathrm{x}}{\mathrm{y}} \\ $$$$\Rightarrow\frac{\mathrm{dy}}{\mathrm{dt}}\:=\:\mathrm{te}^{\mathrm{t}} \Rightarrow\:\mathrm{dy}\:=\:\mathrm{te}^{\mathrm{t}}…