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Category: Differential Equation

x-y-dy-dx-x-2-xy-x-1-

Question Number 92838 by i jagooll last updated on 09/May/20 $$\left(\mathrm{x}+\mathrm{y}\right)\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{x}+\mathrm{1} \\ $$ Commented by john santu last updated on 09/May/20 $$\left(\mathrm{x}+\mathrm{y}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{x}\left(\mathrm{x}+\mathrm{y}\right)+\mathrm{x}+\mathrm{1} \\ $$$$\mathrm{set}\:\mathrm{x}+\mathrm{y}\:=\:\mathrm{v}\:\Rightarrow\mathrm{1}+\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{dv}}{\mathrm{dx}}…

y-y-2y-18te-2t-

Question Number 158309 by cortano last updated on 02/Nov/21 $${y}''+{y}'−\mathrm{2}{y}=−\mathrm{18}{te}^{−\mathrm{2}{t}} \\ $$ Answered by TheSupreme last updated on 02/Nov/21 $$\lambda^{\mathrm{2}} +\lambda−\mathrm{2}=\mathrm{0} \\ $$$$\lambda_{\mathrm{1},\mathrm{2}} =−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{9}}}{\mathrm{2}}=−\mathrm{2},\:\mathrm{1} \\…

Find-dy-dx-x-y-y-x-

Question Number 26983 by chernoaguero@gmail.com last updated on 31/Dec/17 $$\mathrm{Find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\:\: \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} \\ $$ Answered by mrW1 last updated on 31/Dec/17 $${y}\:\mathrm{ln}\:{x}={x}\:\mathrm{ln}\:{y} \\ $$$${y}'\:\mathrm{ln}\:{x}+\frac{{y}}{{x}}=\mathrm{ln}\:{y}+\frac{{x}}{{y}}\:{y}'…