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Category: Differential Equation

solve-the-following-initial-values-DEs-20y-4y-y-0-y-0-3-2-and-y-0-0-

Question Number 98255 by john santu last updated on 12/Jun/20 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{initial}\:\mathrm{values} \\ $$$$\mathrm{DEs}\:\mathrm{20y}''\:+\:\mathrm{4y}'\:+\mathrm{y}\:=\:\mathrm{0} \\ $$$$;\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{3}.\mathrm{2}\:\mathrm{and}\:\mathrm{y}'\left(\mathrm{0}\right)\:=\:\mathrm{0}\: \\ $$ Commented by bemath last updated on 13/Jun/20 $$\mathrm{auxilary}\:\mathrm{equation}\:\mathrm{euler}−\mathrm{cauchy}…

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

Question Number 98106 by bobhans last updated on 11/Jun/20 $$\mathrm{y}''+\mathrm{y}\:=\:\mathrm{cos}\:\mathrm{3x}−\mathrm{2sin}\:\mathrm{3x} \\ $$ Answered by bemath last updated on 11/Jun/20 $$\mathrm{homogenous}\:\mathrm{solution}\: \\ $$$$\lambda^{\mathrm{2}} +\mathrm{1}=\mathrm{0}\:\Rightarrow\lambda\:=\:\pm\:{i} \\ $$$$\mathrm{y}_{\mathrm{h}}…

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}} \\…