Category: Differential Equation

Question Number 210786 by zhou0429 last updated on 19/Aug/24 Answered by Berbere last updated on 19/Aug/24 $$x^9+1=\underset{k=0}{\prod ^8}(x-e^{i\pi \left(\frac{1+2k}{9}\right)})=p\left(x\right)$$$$=\Sigma\int\frac{\mathrm{1}}{\left({x}−{e}^{{i}\pi\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{9}}\right)} \right){p}'\left({e}^{{i}\pi\left(\frac{\mathrm{1}+\mathrm{2}{k}}{\mathrm{9}}\right)} \right)}{dx}…

Question Number 208569 by pticantor last updated on 18/Jun/24 $$\mathit{h}\mathit{e}\mathit{l}\mathit{p}\mathit{m}\mathit{e}\mathit{t}\mathit{o}\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{p}\mathit{l}\mathit{e}\mathit{a}\mathit{s}\mathit{e}$$$${\mathit{y}}^{″}-\sqrt{1+{\mathit{y}}^{\prime 2}}={\mathit{x}}^2$$$$\mathit{s}\mathit{o}\mathit{l}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{i}\mathit{s}\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{t}\mathit{i}\mathit{a}\mathit{l}\mathit{e}\mathit{q}\mathit{u}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$$$$$$$$$$$ Terms of…

Question Number 208264 by efronzo1 last updated on 09/Jun/24 $$\cancel{\underset{―}{\underbrace{}}}$$ Answered by mr W last updated on 10/Jun/24 $$let{y}^{\prime }=p$$$${p}'−\mathrm{2}{p}=\mathrm{2}\left({e}^{{x}} \mathrm{cos}\:{x}−\mathrm{1}\right)…

Question Number 207420 by Wuji last updated on 14/May/24 $$\mathrm{solve}\mathrm{the}\mathrm{Differential}\mathrm{equation}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\left(\frac{\mathrm{x}+3\mathrm{y}}{2\mathrm{x}}\right)$$ Answered by mr W last updated on 14/May/24 $$lety=tx$$$$\frac{{dy}}{{dx}}={t}+{x}\frac{{dt}}{{dx}}…

Question Number 206616 by universe last updated on 20/Apr/24 Answered by aleks041103 last updated on 21/Apr/24 $$e^{3x}isincreasingandcontinuousforx>0$$$$ln\left(x\right)isincr.andcont.forx>0$$$$\Rightarrow f\left(x\right)isincr.andcont.forx>0$$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{f}\left({x}\right)\rightarrow−\infty…