Category: Differential Equation

Question Number 102840 by Dwaipayan Shikari last updated on 11/Jul/20 $$y^{\prime }+\sqrt{x+y-1}=x+y+1$$ Answered by OlafThorendsen last updated on 12/Jul/20 $$y={\mathrm{Y}}^2-x+1$$$$\mathrm{2Y}'\mathrm{Y}−\mathrm{1}+\sqrt{\mathrm{Y}^{\mathrm{2}} }\:=\:\mathrm{Y}^{\mathrm{2}}…

Question Number 168276 by Florian last updated on 07/Apr/22 $$y=\sqrt{x+\sqrt{x+\sqrt{x}}}$$$$y^{\prime }=$$$$$$ Commented by cortano1 last updated on 07/Apr/22 $$\:{y}'=\frac{\mathrm{1}+\frac{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}}{\mathrm{2}\sqrt{{x}+\sqrt{{x}}}}}{\mathrm{2}\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}} \…

Question Number 102716 by Ar Brandon last updated on 10/Jul/20 $${\mathrm{y}}^{″}+{3\mathrm{y}}^{\prime }-10\mathrm{y}={14\mathrm{e}}^{-5\mathrm{x}}$$ Answered by bramlex last updated on 10/Jul/20 $$\mathrm{Homogenous}$$$$\mathrm{r}^{\mathrm{2}} +\mathrm{3r}−\mathrm{10}=\mathrm{0}\:\Rightarrow\left(\mathrm{r}+\mathrm{5}\right)\left(\mathrm{r}−\mathrm{2}\right)=\mathrm{0} \…

Question Number 102527 by bemath last updated on 09/Jul/20 $$2y^{″}-y^{\prime }+y=\cos 3x$$ Answered by Ar Brandon last updated on 09/Jul/20 $$\mathrm{Let}\mathrm{y}=\mathrm{acos}3\mathrm{x}+\mathrm{bsin}3\mathrm{x}$$$$\Rightarrow {\mathrm{y}}^{\prime }=-3\mathrm{asin}3\mathrm{x}+3\mathrm{bcos}3\mathrm{x},{\mathrm{y}}^{″}=-9\mathrm{acos}3\mathrm{x}-9\mathrm{bsin}3\mathrm{x}$$$$\Rightarrow−\mathrm{2}×\mathrm{9}\left(\mathrm{acos3x}+\mathrm{bsin3x}\right)−\mathrm{3}\left(\mathrm{bcos3x}−\mathrm{asin3x}\right)+\mathrm{acos3x}+\mathrm{bsin3x}…

Question Number 102517 by bemath last updated on 09/Jul/20 $$(1+x^2)dy+(1+y^2)dx=0$$ Commented by bemath last updated on 09/Jul/20 Terms of Service Privacy…