Menu Close

Category: Differential Equation

solve-the-o-d-e-1-siny-dx-2ycos-y-x-secy-tany-dy-

Question Number 59872 by necx1 last updated on 15/May/19 $${solve}\:{the}\:{o}\:{d}\:{e} \\ $$$$\left(\mathrm{1}+{siny}\right){dx}=\left\{\mathrm{2}{y}\mathrm{cos}\:{y}−{x}\left({secy}+{tany}\right)\right\}{dy} \\ $$ Answered by ajfour last updated on 15/May/19 $$\frac{\mathrm{dx}}{\mathrm{dy}}+\mathrm{x}\left(\mathrm{sec}\:\mathrm{y}+\mathrm{tan}\:\mathrm{y}\right)=\mathrm{2ycos}\:\mathrm{y} \\ $$$$\mathrm{e}^{\int\frac{\:\mathrm{1}+\mathrm{sin}\:\mathrm{y}}{\mathrm{cos}\:\mathrm{y}}\mathrm{dy}} =\mathrm{e}^{\int\mathrm{tan}\:\frac{\mathrm{y}}{\mathrm{2}}\mathrm{dy}}…

Question-190851

Question Number 190851 by Rupesh123 last updated on 13/Apr/23 Answered by mr W last updated on 13/Apr/23 $$\mathrm{cos}\:{y}'=\mathrm{sin}\:{y} \\ $$$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−{y}'\right)=\mathrm{sin}\:{y} \\ $$$$\frac{\pi}{\mathrm{2}}−{y}'={n}\pi+\left(−\mathrm{1}\right)^{{n}} {y} \\ $$$$−{y}'=\left(−\mathrm{1}\right)^{{n}}…

Find-dy-dx-from-first-principle-if-y-sin-2-x-

Question Number 59720 by Tawa1 last updated on 13/May/19 $$\mathrm{Find}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:\mathrm{from}\:\mathrm{first}\:\mathrm{principle},\:\:\mathrm{if}\:\:\:\:\mathrm{y}\:=\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right) \\ $$ Commented by maxmathsup by imad last updated on 14/May/19 $$\frac{{dy}}{{dx}}\:=\mathrm{2}{sinx}\:{cosx}\:\:={sin}\left(\mathrm{2}{x}\right). \\ $$…