Category: Differential Equation

Question Number 163113 by Lordose last updated on 03/Jan/22 $$\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}+\mathrm{ytan}\left(\mathrm{x}\right)={\mathrm{e}}^{\mathrm{x}}\mathrm{y}\left(0\right)=1,{\mathrm{y}}^{\prime }\left(0\right)=0$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 97266 by bobhans last updated on 07/Jun/20 $$\mathrm{If}\mathrm{x}\mathrm{\&}\mathrm{y}\mathrm{satisfy}\mathrm{the}\mathrm{equation}{\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}-6\mathrm{y}-1=0$$$$\mathrm{find}\mathrm{minimum}\mathrm{value}\mathrm{of}\mathrm{x}+\mathrm{y}?$$ Commented by bobhans last updated on 07/Jun/20 $$\mathrm{f}\left(\mathrm{x},\mathrm{y},\lambda\right)\:=\:\mathrm{x}+\mathrm{y}+\lambda\left(\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}}…

Question Number 97001 by bemath last updated on 06/Jun/20 $$\mathrm{solve}(1+{\mathrm{x}}^2)\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{xy}-{\mathrm{xy}}^2$$ Commented by bobhans last updated on 06/Jun/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{x}\left(\mathrm{y}−\mathrm{y}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\Leftrightarrow\:\frac{\mathrm{dy}}{\mathrm{y}−\mathrm{y}^{\mathrm{2}} }\:=\:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}…

Question Number 96669 by john santu last updated on 03/Jun/20 $$\mathrm{find}\mathrm{minimum}\mathrm{value}$$$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{{\mathrm{x}}^2+9}+\sqrt{{\mathrm{x}}^2-30\mathrm{x}+250}$$ Answered by bemath last updated on 03/Jun/20 $$\mathrm{17}?…

Question Number 96596 by bemath last updated on 03/Jun/20 $$x(x+1)\frac{dy}{dx}-(2x+1)y=0$$ Answered by bobhans last updated on 03/Jun/20 $$\frac{dy}{dx}=\frac{2x+1}{x^2+x}.y\Rightarrow \frac{dy}{y}=\frac{(2x+1)dx}{x^2+x}$$$$\mathrm{ln}\mid\mathrm{y}\mid\:=\:\mathrm{ln}\mid\mathrm{C}\left({x}^{\mathrm{2}} +{x}\right)\mid\:\Rightarrow\:\mathrm{y}=\:\mathrm{C}\left({x}^{\mathrm{2}}…