Menu Close

Category: Differential Equation

Solve-xy-y-sin-x-y-5-0-

Question Number 70232 by Joel122 last updated on 02/Oct/19 $$\mathrm{Solve} \\ $$$${xy}'\:−\:{y}\:\mathrm{sin}\:{x}\:+\:{y}^{\mathrm{5}} \:=\:\mathrm{0} \\ $$ Commented by Joel122 last updated on 02/Oct/19 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Bernoulli}'\mathrm{s}\:\mathrm{equation} \\ $$$${y}'\:−\:\left(\frac{\mathrm{sin}\:{x}}{{x}}\right){y}\:=\:−\frac{{y}^{\mathrm{5}}…

Solve-the-following-system-of-differential-equations-for-functions-x-t-and-y-t-m-d-2-x-dt-2-kx-x-2-y-2-2-m-d-2-y-dt-2-ky-x-2-y-2-2-

Question Number 4625 by Yozzis last updated on 14/Feb/16 $${Solve}\:{the}\:{following}\:{system}\:{of}\:{differential}\: \\ $$$${equations}\:{for}\:{functions}\:{x}\left({t}\right)\:{and}\:{y}\left({t}\right). \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }=\frac{{kx}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}\frac{{d}^{\mathrm{2}} {y}}{{dt}^{\mathrm{2}} }=\frac{{ky}}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)^{\mathrm{2}}…

Give-an-example-of-differential-equation-which-has-no-solutions-

Question Number 3656 by prakash jain last updated on 17/Dec/15 $$\mathrm{Give}\:\mathrm{an}\:\mathrm{example}\:\mathrm{of}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{which} \\ $$$$\mathrm{has}\:\mathrm{no}\:\mathrm{solutions}. \\ $$ Answered by Filup last updated on 18/Dec/15 $${Weierstrass}\:{function} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{fuction}\:\mathrm{that}\:\mathrm{is}\:\mathrm{continuous}\:\mathrm{at}\:\mathrm{all}…

sin-4-xdx-

Question Number 134694 by Engr_Jidda last updated on 06/Mar/21 $$\int{sin}^{\mathrm{4}} {xdx} \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\mathcal{J}\:=\:\int\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} {dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\int\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} \:{dx}…