Category: Differential Equation

Question Number 118274 by bobhans last updated on 16/Oct/20 $$y^{″}-3y^{\prime }+2y=\frac{1}{1+e^{-x}}$$ Answered by mathmax by abdo last updated on 16/Oct/20 $$\mathrm{h}\rightarrow\mathrm{r}^{\mathrm{2}} −\mathrm{3r}+\mathrm{2}=\mathrm{0}\:\rightarrow\Delta=\mathrm{9}−\mathrm{8}=\mathrm{1}\:\Rightarrow\mathrm{r}_{\mathrm{1}} =\frac{\mathrm{3}+\mathrm{1}}{\mathrm{2}}=\mathrm{2}\:\mathrm{and}\:\mathrm{r}_{\mathrm{2}}…

Question Number 183638 by ali009 last updated on 27/Dec/22 $$findy\left(t\right)$$$$y\left(t\right)+2e^t{\int }_0^t(y\left(\tau \right)-e^{-\tau })d\tau ={te}^t$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 183532 by MikeH last updated on 26/Dec/22 Answered by CElcedricjunior last updated on 26/Dec/22 $$3{\mathit{x}\mathit{y}}^{\prime }-\mathit{y}=\mathit{l}\mathit{n}\mathit{x}+1\mathit{y}\left(1\right)=-2$$$$\left(\mathit{h}\right):3{\mathit{x}\mathit{y}}^{\prime }-\mathit{y}=0=>\mathit{y}={\mathit{e}}^{\int \frac{1}{3\mathit{x}}\mathit{d}\mathit{x}}={\mathit{k}\mathit{e}}^{\frac{1}{3}\mathit{l}\mathit{n}\mid \mathit{x}\mid }={\mathit{k}\mathit{e}}^{\frac{1}{3}\mathit{l}\mathit{n}\mathit{x}}\mathit{p}\mathit{o}\mathit{u}\mathit{r}\mathit{x}\in {\mathbb{R}}_{+}^{\ast }$$$$\boldsymbol{{y}}=\boldsymbol{{k}}\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}}…

Question Number 52208 by SUJIT420 last updated on 04/Jan/19 Commented by maxmathsup by imad last updated on 04/Jan/19 $$itsnotcitse.$$ Commented by maxmathsup by…

Question Number 117632 by syamil last updated on 12/Oct/20 $$Solutionfrom2xydy=(x^2-y^2)dx$$ Answered by 1549442205PVT last updated on 13/Oct/20 $$\:\mathrm{2}{xy}\:{dy}\:=\:\left({x}^{\mathrm{2}\:} \:−\:{y}^{\mathrm{2}} \right){dx} \…