Category: Differential Equation

Question Number 121687 by abdelsalamalmukasabe last updated on 10/Nov/20 Commented by bemath last updated on 11/Nov/20 $$\left(\frac{2y^4+1}{y^2}\right)dx+\left(4xy\right)dy=0$$$$(2y^4+1)dx+\left(4{xy}^3\right)dy=0$$$$\Rightarrow\:\frac{{dy}}{{dx}}\:=\:\frac{−\left(\mathrm{2}{y}^{\mathrm{4}}…

Question Number 121609 by benjo_mathlover last updated on 10/Nov/20 $$\mathrm{y}\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2}\mathrm{dx}-\mathrm{x}(\mathrm{x}+\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2})\mathrm{dy}=0$$$$$$ Answered by liberty last updated on 10/Nov/20…

Question Number 55939 by MJS last updated on 06/Mar/19 $$\frac{y^{\prime }}{y}=1-\cot x$$$$y=?$$ Answered by kaivan.ahmadi last updated on 06/Mar/19 $$\frac{1}{y}\frac{dy}{dx}=1-cotx\Rightarrow$$$$\frac{\mathrm{1}}{{y}}{dy}=\left(\mathrm{1}−{cotx}\right){dx}\Rightarrow \…

Question Number 121461 by bramlexs22 last updated on 08/Nov/20 Answered by Olaf last updated on 08/Nov/20 $$(3y^2+10{xy}^2)dx+(6xy-2+10x^{2}y)dy=0$$$$\mathrm{d}f=\frac{\partial f}{\partial x}(x,y)dx+\frac{\partial f}{\partial y}(x,y)dy=0$$$$ \…

Question Number 121227 by benjo_mathlover last updated on 06/Nov/20 $$\frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}={\mathrm{e}}^{-2\mathrm{x}}$$ Answered by Lordose last updated on 06/Nov/20 $$\frac{\mathrm{dy}}{\mathrm{dx}}=\:\int\mathrm{e}^{−\mathrm{2x}} \mathrm{dx} \…