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Category: Differential Equation

x-2-x-d-2-y-dx-2-1-2x-2-dy-dx-x-2-x-1-y-x-2-x-1-

Question Number 97847 by bemath last updated on 10/Jun/20 $$\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}\right)\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\left(\mathrm{1}−\mathrm{2x}^{\mathrm{2}} \right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}\right)\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1} \\ $$ Answered by niroj last updated on 10/Jun/20…

y-2-xy-dx-2xy-dy-0-

Question Number 97751 by bobhans last updated on 09/Jun/20 $$\left(\mathrm{y}^{\mathrm{2}} −\mathrm{xy}\right)\mathrm{dx}\:+\:\mathrm{2xy}\:\mathrm{dy}\:=\:\mathrm{0}\: \\ $$ Commented by bemath last updated on 09/Jun/20 $$\Leftrightarrow\:\mathrm{2xy}\:\mathrm{dy}\:=\:\left(\mathrm{xy}−\mathrm{y}^{\mathrm{2}} \right)\:\mathrm{dx}\: \\ $$$$\mathrm{set}\:\mathrm{y}\:=\:\mathrm{zx}\:\Leftrightarrow\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{z}\:+\:\mathrm{x}\:\frac{\mathrm{dz}}{\mathrm{dx}} \\…

If-x-amp-y-satisfy-the-equation-x-2-y-2-4x-6y-1-0-find-minimum-value-of-x-y-

Question Number 97266 by bobhans last updated on 07/Jun/20 $$\mathrm{If}\:\mathrm{x}\:\&\mathrm{y}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{4x}−\mathrm{6y}−\mathrm{1}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}\:? \\ $$ Commented by bobhans last updated on 07/Jun/20 $$\mathrm{f}\left(\mathrm{x},\mathrm{y},\lambda\right)\:=\:\mathrm{x}+\mathrm{y}+\lambda\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}}…

solve-1-x-2-dy-dx-xy-xy-2-

Question Number 97001 by bemath last updated on 06/Jun/20 $$\mathrm{solve}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{xy}−\mathrm{xy}^{\mathrm{2}} \\ $$ Commented by bobhans last updated on 06/Jun/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}\left(\mathrm{y}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\Leftrightarrow\:\frac{\mathrm{dy}}{\mathrm{y}−\mathrm{y}^{\mathrm{2}} }\:=\:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}…