Category: Differential Equation

Question Number 15942 by Don sai last updated on 15/Jun/17 $$\mathrm{Help}.$$$$\mathrm{solve}(\mathrm{x}+2)\mathrm{dy}/\mathrm{dx}=3-2\mathrm{y}/\mathrm{x}$$ Answered by mrW1 last updated on 16/Jun/17 $$(\mathrm{x}+2)\frac{\mathrm{dy}}{\mathrm{dx}}+\frac{2}{\mathrm{x}}\mathrm{y}=3$$$$\frac{\mathrm{dy}}{\mathrm{dx}}+\frac{\mathrm{2}}{\mathrm{x}\left(\mathrm{x}+\mathrm{2}\right)}\mathrm{y}=\frac{\mathrm{3}}{\mathrm{x}+\mathrm{2}}…

Question Number 15840 by tawa tawa last updated on 14/Jun/17 $$\mathrm{Solve}\mathrm{the}\mathrm{ODE}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}+{\mathrm{x}}^2\mathrm{y}={\mathrm{x}}^4$$$$$$ Commented by chux last updated on 14/Jun/17…

Question Number 15707 by Joel577 last updated on 13/Jun/17 $$x^3+{(y+1)}^2.\frac{dy}{dx}=0$$$$\mathrm{Find}y$$ Answered by ajfour last updated on 13/Jun/17 $$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} {dx}+\left({y}+\mathrm{1}\right)^{\mathrm{2}}…

Question Number 81157 by ~blr237~ last updated on 09/Feb/20 $$Letn⩾2,forx\in [0,1]:letconsiderA\left(x\right)=\{u\in {\mathbb{R}}_{+}^{\ast }\mathrm{\setminus }x<u^n\}$$$$1)Provethatifa,b\in [0,1]a⩽b\iff A\left(a\right)\subseteq A\left(b\right)$$$$2)Deducex={\left[infA\left(x\right)\right]}^n$$ Terms of Service Privacy Policy…

Question Number 15095 by tawa tawa last updated on 07/Jun/17 $$\mathrm{Solve}:$$$$(1-\mathrm{x})\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{y}(1+\mathrm{x})$$ Answered by Tinkutara last updated on 07/Jun/17 $$\frac{dy}{y}=\frac{1+x}{1-x}dx=(-1-\frac{2}{x-1})dx$$$$\mathrm{ln}\:{y}\:=\:−{x}\:−\:\mathrm{2}\:\mathrm{ln}\:\mid{x}\:−\:\mathrm{1}\mid\:+\:{C}…