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Category: Differential Equation

find-d-4-y-dx-4-d-3-y-dx-3-7-d-2-y-dx-2-dy-dx-6y-0-for-y-0-1-y-0-0-y-0-2-y-0-1-

Question Number 125693 by fajri last updated on 13/Dec/20 $${find}\:: \\ $$$$ \\ $$$$\frac{{d}^{\mathrm{4}} {y}}{{dx}^{\mathrm{4}} }\:+\:\frac{{d}^{\mathrm{3}} {y}}{{dx}^{\mathrm{3}} }\:−\:\mathrm{7}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\:\frac{{dy}}{{dx}\:\:}\:+\:\mathrm{6}{y}\:=\:\mathrm{0} \\ $$$$ \\ $$$${for}\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1},\:{y}'\left(\mathrm{0}\right)\:=\:\mathrm{0},\:{y}''\left(\mathrm{0}\right)\:=\:−\mathrm{2}\:,\:{y}'''\left(\mathrm{0}\right)\:=\:−\mathrm{1} \\…

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}}…