Category: Differentiation

Question Number 63894 by mathmax by abdo last updated on 10/Jul/19 $$sovethe\left(de\right)x^2{y}^{{}^{\prime }}-(2x+3)y=sin\left(x^2\right)withy\left(1\right)=2and$$$$y^{{}^{\prime }}\left(1\right)=1.$$ Commented by mathmax by abdo…

Question Number 63824 by mathmax by abdo last updated on 10/Jul/19 $$solve{y}^{{}^{\prime }}\sqrt{2x-1}+y(x^2+3)=xsin\left(2x\right)$$ Commented by mathmax by abdo last updated on 12/Jul/19…

Question Number 129319 by snipers237 last updated on 14/Jan/21 $$Provethat$$$$iffissuchasf{}^{\prime }\left(x\right)=\frac{f\left(x\right)}{x(1-x-f\left(x\right))}$$$$andf\left(1\right)=0butf\ncong \mathrm{\Theta }.Then$$$$★fistheuniquebijectionfrom{\mathbb{R}}^{\ast }to\mathbb{R}and$$$$★\underset{x\to 0}{\lim }f\left(x\right)=+\mathrm{\infty }and\underset{x\to 0}{\lim }xf\left(x\right)=0$$$$\:\bigstar\:\int_{\mathrm{0}} ^{+\infty} {f}^{−\mathrm{1}}…

Question Number 129272 by mnjuly1970 last updated on 14/Jan/21 $$\dots nicecalculus\dots$$$$evsluate::$$$$\mathrm{\Omega }=\underset{n=0}{\sum ^{\mathrm{\infty }}}{(-1)}^n\left(\frac{\mathrm{\Gamma }(n+\frac{3}{2})}{2^n\mathrm{\Gamma }(2n+2)}\right)=???$$$$$$ Answered by Dwaipayan…

Question Number 129171 by benjo_mathlover last updated on 13/Jan/21 $$\sqrt{1-{\mathrm{y}}^2}\mathrm{dx}-\sqrt{1-{\mathrm{x}}^2}\mathrm{dy}=0$$$$\mathrm{y}\left(0\right)=\frac{\sqrt{3}}{2}$$ Answered by bramlexs22 last updated on 13/Jan/21 $$\:\Rightarrow\:\sqrt{\mathrm{1}−\mathrm{y}^{\mathrm{2}} }\:\mathrm{dx}\:=\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}}…