Category: Differential Equation

Question Number 102298 by Ar Brandon last updated on 08/Jul/20 $$\mathrm{sinx}\cdot \frac{\mathrm{dy}}{\mathrm{dx}}-\mathrm{ycosx}={\mathrm{y}}^3{\sin }^2\mathrm{xcosx}$$ Answered by john santu last updated on 08/Jul/20 $$\frac{{dy}}{{dx}}−{y}\mathrm{cot}\:{x}=\mathrm{sin}\:{x}\mathrm{cos}\:{x}\:.{y}^{\mathrm{3}} \…

Question Number 102283 by Ar Brandon last updated on 08/Jul/20 $$\mathrm{sinx}\frac{\mathrm{dy}}{\mathrm{dx}}-2\mathrm{ycosx}=3\mathrm{sinx}$$ Answered by john santu last updated on 08/Jul/20 $$\frac{dy}{dx}-2\cot x.y=3$$$${IF}\:\Rightarrow{u}\left({x}\right)={e}^{\int\:−\mathrm{2cot}\:{x}\:{dx}\:} =\:{e}^{−\mathrm{2ln}\left(\mathrm{sin}\:{x}\right)}…

Question Number 101841 by bemath last updated on 05/Jul/20 $${xy}^{\prime }+y=y^2$$ Answered by bobhans last updated on 05/Jul/20 $${xy}^{\prime }=y^2-y\Rightarrow \frac{dy}{y(y-1)}=\frac{dx}{x}$$$$\int \frac{dy}{y-1}-\int \frac{dy}{y}=\frac{dx}{x}$$$$\mathrm{ln}\left(\frac{{y}−\mathrm{1}}{{y}}\right)\:=\:\mathrm{ln}\mid{Cx}\mid\:\Rightarrow\:\mathrm{1}−\frac{\mathrm{1}}{{y}}\:=\:\mid{Cx}\mid\:…

Question Number 101777 by 1549442205 last updated on 04/Jul/20 $$\mathrm{Find}\mathrm{a}\mathrm{curve}\mathrm{passing}\mathrm{through}\mathrm{pointA}(0;1)$$$$\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{triangle}\mathrm{formed}\mathrm{by}\mathrm{the}\mathrm{axis}\mathrm{Oy}$$$$,\mathrm{tangent}\mathrm{to}\mathrm{the}\mathrm{curve}\mathrm{at}\mathrm{its}\mathrm{arbitrary}\mathrm{point}$$$$\mathrm{and}\mathrm{the}\mathrm{radius}-\mathrm{vector}\mathrm{of}\mathrm{the}\mathrm{point}\mathrm{of}$$$$\mathrm{contact},\mathrm{issosceles}(\mathrm{and}\mathrm{base}\mathrm{is}\mathrm{the}\mathrm{segment}$$$$\mathrm{of}\mathrm{the}\mathrm{tangent}\mathrm{from}\mathrm{the}\mathrm{point}\mathrm{of}\mathrm{contact}$$$$\mathrm{to}\mathrm{the}\mathrm{axis}\mathrm{Oy})$$ Terms…

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}}…