Category: Differential Equation

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

Question Number 104669 by bramlex last updated on 23/Jul/20 $$(x^2+y^2)dy=xydx$$ Answered by bemath last updated on 23/Jul/20 $$sety=zx$$$$\frac{{dy}}{{dx}}\:=\:{z}\:+\:{x}\:\frac{{dz}}{{dx}} \…

Question Number 104651 by Ar Brandon last updated on 23/Jul/20 $$\mathrm{Consider}\mathrm{the}\mathrm{differential}\mathrm{equation};$$$${\mathrm{x}}^{″}\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)={\mathrm{t}}^2\cos \left(2\mathrm{t}\right).$$$$\mathrm{Knowing}\mathrm{that}\mathrm{the}\mathrm{Complementary}\mathrm{Function}\mathrm{is};$$$${\mathrm{y}}_{\mathrm{CF}}=\mathrm{acos}\left(\mathrm{t}\right)+\mathrm{bsin}\left(\mathrm{t}\right),$$$$\mathrm{In}\mathrm{what}\mathrm{form}\mathrm{can}\mathrm{the}\mathrm{particular}\mathrm{integral}\mathrm{be}\mathrm{expressed}$$$$\mathrm{so}\mathrm{as}\mathrm{to}\mathrm{obtain}\mathrm{the}\mathrm{general}\mathrm{solution}\mathrm{to}\mathrm{the}\mathrm{given}$$$$\mathrm{differential}\:\mathrm{equation}?…

Question Number 104595 by Ar Brandon last updated on 22/Jul/20 $$\mathrm{Solve}\mathrm{the}\mathcal{DE}$$$${\mathrm{x}}^{″}\left(\mathrm{t}\right)+{2\mathrm{x}}^{\prime }\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)={\mathrm{te}}^{-\mathrm{t}}$$ Answered by mathmax by abdo last updated on 22/Jul/20 $$\left.\mathrm{h}\right)\rightarrow\mathrm{r}^{\mathrm{2}}…

Question Number 170116 by ali009 last updated on 16/May/22 $$solvetheD.E.$$$$(x+2y-4)dx+(2x+y-5)dy=0$$ Commented by mr W last updated on 17/May/22 $$seeQ169558$$…