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Question-96428

Question Number 96428 by Hassanfathi last updated on 01/Jun/20 Answered by Sourav mridha last updated on 01/Jun/20 $$\boldsymbol{{y}}^{''} \left(\boldsymbol{{t}}\right)−\mathrm{3}\boldsymbol{{y}}^{'} \left(\mathrm{t}\right)+\mathrm{2}\boldsymbol{{y}}\left(\boldsymbol{{t}}\right)=\mathrm{4} \\ $$$$\boldsymbol{{using}}\:\boldsymbol{{Laplace}}\:\boldsymbol{{transform}} \\ $$$$\boldsymbol{{s}}^{\mathrm{2}} \boldsymbol{{y}}\left(\boldsymbol{{s}}\right)−\boldsymbol{{sy}}\left(\mathrm{0}\right)−\boldsymbol{{y}}^{'}…

Question-96429

Question Number 96429 by Hassanfathi last updated on 01/Jun/20 Answered by abdomathmax last updated on 01/Jun/20 $$\mathrm{y}^{\left(\mathrm{3}\right)} \:+\mathrm{y}^{\left(\mathrm{1}\right)} \:=\mathrm{t}+\mathrm{1}\:\Rightarrow \\ $$$$\mathrm{L}\left(\mathrm{y}^{\left(\mathrm{3}\right)} \right)+\mathrm{L}\left(\mathrm{y}^{\left(\mathrm{1}\right)} \right)\:=\mathrm{L}\left(\mathrm{t}+\mathrm{1}\right)\:\Rightarrow \\ $$$$\mathrm{t}^{\mathrm{3}}…

Question-96419

Question Number 96419 by Hassanfathi last updated on 01/Jun/20 Commented by bemath last updated on 01/Jun/20 $$\left(\mathrm{2}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{ky}\:=\mathrm{e}^{\mathrm{2kx}} \\ $$$$\mathrm{IF}\:\mathrm{u}\left(\mathrm{x}\right)\:=\:\mathrm{e}^{\int\mathrm{k}\:\mathrm{dx}} \:=\:\mathrm{e}^{\mathrm{kx}} \\ $$$$\Rightarrow\mathrm{e}^{\mathrm{kx}} \frac{\mathrm{dy}}{\mathrm{dx}}+\:\mathrm{ke}^{\mathrm{kx}} \mathrm{y}\:=\:\mathrm{e}^{\mathrm{3kx}} \\…

Prove-that-0-xcos-x-sin-x-2-x-6-dx-15-

Question Number 161945 by Ahmed777hamouda last updated on 24/Dec/21 $$\:\:\boldsymbol{{P}\mathrm{rove}}\:\boldsymbol{\mathrm{that}}\:\int_{\mathrm{0}} ^{\infty} \frac{\left(\boldsymbol{{xcos}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)^{\mathrm{2}} }{\boldsymbol{{x}}^{\mathrm{6}} }\boldsymbol{{dx}}\:=\frac{\boldsymbol{\pi}}{\mathrm{15}} \\ $$ Answered by Ar Brandon last updated on 24/Dec/21 $${I}=\int_{\mathrm{0}}…