Category: Differential Equation

Question Number 103776 by bemath last updated on 17/Jul/20 $$y^{\prime }-\frac{y}{x^2-1}=y^2$$ Answered by bemath last updated on 17/Jul/20 $$setv=y^{-1}\Rightarrow \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}$$$$\frac{{dy}}{{dx}}\:=\:−{y}^{\mathrm{2}}…

Question Number 103769 by bemath last updated on 17/Jul/20 $$2y^{″}-y^{\prime }+y=\cos 3x$$ Answered by mathmax by abdo last updated on 17/Jul/20 $$\mathrm{let}\mathrm{solve}\mathrm{by}\mathrm{laplace}\mathrm{transform}$$$$\mathrm{e}\:\Rightarrow\mathrm{2L}\left(\mathrm{y}^{''} \right)−\mathrm{L}\left(\mathrm{y}^{'}…

Question Number 103759 by bemath last updated on 17/Jul/20 $$(x^5+3y)dx-xdy=0$$ Answered by MAB last updated on 17/Jul/20 $$x^5+3y-{xy}^{\prime }=0$$$${xy}'−\mathrm{3}{y}={x}^{\mathrm{5}} \…

Question Number 103664 by byaw last updated on 16/Jul/20 Answered by bramlex last updated on 16/Jul/20 $$({\mathrm{x}}^2+{\mathrm{y}}^2)\mathrm{dx}=2\mathrm{xy}\mathrm{dy}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\mathrm{x}}^2+{\mathrm{y}}^2}{2\mathrm{xy}};\mathrm{set}\mathrm{y}=\mathrm{zx}$$$$\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{z}\:+\:\mathrm{x}\:\frac{\mathrm{dz}}{\mathrm{dx}}…

Question Number 169155 by Mastermind last updated on 27/Apr/22 $$\left(3\right)Considertheboundary-value$$$$problem{y}^{″}+2y^{\prime }+2y=0,y\left(a\right)=c,$$$$y\left(b\right)=d.\left(i\right)ifthisproblemhasa$$$$uniquesolution,howareaandb$$$$related?\left(ii\right)ifthisproblemhasno$$$$solution,howarea,b,canddrelated?$$ Terms of Service…