Menu Close

Category: Differential Equation

solve-y-y-x-1-x-y-2-1-

Question Number 104845 by john santu last updated on 24/Jul/20 $${solve}\:{y}'\:=\:{y}−{x}−\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$ Answered by john santu last updated on 24/Jul/20 $$\frac{{dy}}{{dx}}\:=\:−\left({x}−{y}+\mathrm{2}\right)+\mathrm{1}+\left({x}−{y}+\mathrm{2}\right)^{−\mathrm{1}} \\ $$$${set}\:{x}−{y}+\mathrm{2}\:=\:{m}\: \\…

Consider-the-differential-equation-x-t-x-t-t-2-cos-2t-Knowing-that-the-Complementary-Function-is-y-CF-acos-t-bsin-t-In-what-form-can-the-particular-integral-be-expressed-so-as-to-obtain-

Question Number 104651 by Ar Brandon last updated on 23/Jul/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{2t}\right). \\ $$$$\mathrm{Knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Complementary}\:\mathrm{Function}\:\mathrm{is}; \\ $$$$\mathrm{y}_{\mathrm{CF}} =\mathrm{acos}\left(\mathrm{t}\right)+\mathrm{bsin}\left(\mathrm{t}\right), \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{form}\:\mathrm{can}\:\mathrm{the}\:\mathrm{particular}\:\mathrm{integral}\:\mathrm{be}\:\mathrm{expressed} \\ $$$$\mathrm{so}\:\mathrm{as}\:\mathrm{to}\:\mathrm{obtain}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{to}\:\mathrm{the}\:\mathrm{given}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}?…