Category: Differential Equation

Question Number 98808 by bemath last updated on 16/Jun/20 Answered by john santu last updated on 16/Jun/20 $$y=wx\Rightarrow \frac{dy}{dx}=w+x\frac{dw}{dx}$$$$\Leftrightarrow{w}\:+\:{x}\:\frac{{dw}}{{dx}}\:=\:\frac{{wx}^{\mathrm{2}} −{w}^{\mathrm{2}} {x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{wx}^{\mathrm{2}} }…

Question Number 98367 by bobhans last updated on 13/Jun/20 $$\mathrm{show}\mathrm{that}\phi \left(\mathrm{x}\right)={\mathrm{x}}^2-{\mathrm{x}}^{-1}\mathrm{is}\mathrm{an}\mathrm{explicit}$$$$\mathrm{solution}\mathrm{to}\mathrm{linear}\mathrm{equation}\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}-\frac{2\mathrm{y}}{{\mathrm{x}}^2}=0$$ Commented by john santu last updated…

Question Number 98106 by bobhans last updated on 11/Jun/20 $${\mathrm{y}}^{″}+\mathrm{y}=\cos 3\mathrm{x}-2\sin 3\mathrm{x}$$ Answered by bemath last updated on 11/Jun/20 $$\mathrm{homogenous}\mathrm{solution}$$$${\lambda }^2+1=0\Rightarrow \lambda =\pm i$$$$\mathrm{y}_{\mathrm{h}}…

Question Number 97922 by bemath last updated on 10/Jun/20 $${\mathrm{y}}^{″}+\mathrm{y}=\cot x$$ Answered by bobhans last updated on 10/Jun/20 Commented by bemath last updated on…

Question Number 97866 by me2love2math last updated on 10/Jun/20 Commented by me2love2math last updated on 10/Jun/20 $$125and6$$ Commented by bobhans last updated on…