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Category: Differential Equation

Solve-the-differential-equations-i-x-2-d-2-y-dx-2-x-dy-dx-y-log-x-ii-x-2-2-d-2-y-dx-2-4-x-2-dy-dx-6y-x-

Question Number 86640 by niroj last updated on 29/Mar/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\left(\boldsymbol{\mathrm{i}}\right).\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\boldsymbol{\mathrm{x}}\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\:\boldsymbol{\mathrm{y}}\:=\:\:\boldsymbol{\mathrm{log}}\:\boldsymbol{\mathrm{x}}. \\ $$$$\:\:\left(\boldsymbol{\mathrm{ii}}\right).\:\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)^{\mathrm{2}} \:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\:\mathrm{4}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\:\mathrm{6}\boldsymbol{\mathrm{y}}\:=\:\:\boldsymbol{\mathrm{x}}. \\ $$$$\: \\ $$ Answered…

Solve-the-following-equation-d-2-y-dx-2-2-dy-dx-y-x-e-x-sin-x-

Question Number 86307 by niroj last updated on 28/Mar/20 $$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:−\mathrm{2}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:+\boldsymbol{\mathrm{y}}\:=\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \:\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}. \\ $$ Answered by TANMAY PANACEA. last updated on 28/Mar/20…

y-sin-t-cos-t-y-sin-3-t-y-pi-4-0-

Question Number 86142 by jagoll last updated on 27/Mar/20 $$\mathrm{y}'\:.\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=\:\mathrm{y}\:+\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{t}\: \\ $$$$\mathrm{y}\left(\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{0}\: \\ $$ Answered by Kunal12588 last updated on 27/Mar/20 $$\frac{{dy}}{{dt}}=\frac{{y}}{\mathrm{sin}\:{t}\:\mathrm{cos}\:{t}}+\mathrm{sin}\:{t}\:\mathrm{tan}\:{t} \\ $$$$\Rightarrow\frac{{dy}}{{dt}}+\left(−\frac{\mathrm{1}}{\mathrm{sin}\:{t}\:\mathrm{cos}\:{t}}\right){y}=\mathrm{sin}\:{t}\:\mathrm{tan}\:{t}…

dy-dx-1-sin-x-2y-

Question Number 85766 by jagoll last updated on 24/Mar/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{1}−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{2y}\right) \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\mathrm{u}\:=\:\mathrm{x}+\mathrm{2y} \\ $$$$\frac{\mathrm{du}}{\mathrm{dx}}\:=\:\mathrm{1}+\mathrm{2}\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\frac{\mathrm{2dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{du}}{\mathrm{dx}}−\mathrm{1}\:\Rightarrow\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\:\frac{\mathrm{du}}{\mathrm{dx}}−\mathrm{1}\right] \\…