Category: Differential Equation

Question Number 101680 by john santu last updated on 04/Jul/20 Answered by bemath last updated on 04/Jul/20 $$\mathrm{let}\mathrm{point}\mathrm{R}(\mathrm{x},{\mathrm{x}}^2)$$$$\mathrm{area}\mathrm{of}\mathrm{\Delta }\mathrm{PQR}=\frac{1}{2}\left|\begin{array}{c}241\\ -111\\ \mathrm{x}{\mathrm{x}}^{2}1\end{array}\right|$$$$\mathrm{A}\left(\mathrm{x}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}\left\{\mathrm{2}\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)−\mathrm{4}\left(−\mathrm{1}−\mathrm{x}\right)+\mathrm{1}\left(−\mathrm{x}^{\mathrm{2}}…

Question Number 101362 by bobhans last updated on 02/Jul/20 Commented by bemath last updated on 02/Jul/20 $$({\mathrm{x}}^2+{3\mathrm{y}}^2)\mathrm{dx}+(2\mathrm{xy}-\mathrm{x})\mathrm{dy}=0$$$$\mathrm{M}={\mathrm{x}}^2+{3\mathrm{y}}^2\to \frac{\partial \mathrm{M}}{\partial \mathrm{y}}=6\mathrm{y}$$$$\mathrm{N}\:=\:\mathrm{2xy}−\mathrm{x}\rightarrow\frac{\partial\mathrm{N}}{\partial\mathrm{x}}\:=\:\mathrm{2y}−\mathrm{1}…

Question Number 166764 by amin96 last updated on 27/Feb/22 $$\frac{\mathbf{dy}}{\mathbf{dx}}=\mathbf{cos}(\mathbf{y}-\mathbf{x})$$ Answered by mr W last updated on 27/Feb/22 $$letu=y-x$$$$y=u+x$$$$\frac{{dy}}{{dx}}=\frac{{du}}{{dx}}+\mathrm{1}…

Question Number 100891 by bemath last updated on 29/Jun/20 $${\mathrm{u}}_{\mathrm{tt}}={\mathrm{u}}_{\mathrm{xx}}-6\mathrm{x};0⩽\mathrm{x}<\pi ,\mathrm{t}>0$$$${\mathrm{u}}_{(0,\mathrm{t})}=0;{\mathrm{u}}_{(\pi ,\mathrm{t})}={\pi }^3+3\pi$$$${\mathrm{u}}_{(\mathrm{x},0)}={\mathrm{x}}^3+3\mathrm{x}+3\sin \mathrm{x}$$$$\mathrm{u}_{\mathrm{t}} \left(\mathrm{x},\mathrm{0}\right)\:=\:\mathrm{0}\: \…

Question Number 100684 by bemath last updated on 28/Jun/20 $$({\mathrm{x}}^2+\mathrm{xy})\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{xy}+{\mathrm{y}}^2$$ Answered by bobhans last updated on 28/Jun/20 $$\mathrm{set}\mathrm{y}=\mathrm{sx}\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{s}+\mathrm{x}\frac{\mathrm{ds}}{\mathrm{dx}}$$$$\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \mathrm{s}\right)\:\left(\mathrm{s}\:+\mathrm{x}\:\frac{\mathrm{ds}}{\mathrm{dx}}\right)\:=\:\mathrm{x}^{\mathrm{2}}…