2.472   ODE No. 472

1. Problem in Latex
2. Mathematica input
3. Maple input

$$(y(x)+x)y^{\prime }(x{)}^2+2x{y}^{\prime }(x)-y(x)=0$$ ✓ Mathematica : cpu = 0.185848 (sec), leaf count = 127

$$\{\{y(x)\to \frac{1}{3}(-2\sqrt{e^{2c_1}-3e^{c_1}x}-e^{c_1})\},\{y(x)\to \frac{1}{3}(2\sqrt{e^{2c_1}-3e^{c_1}x}-e^{c_1})\},\{y(x)\to e^{c_1}-2\sqrt{e^{c_1}x+e^{2c_1}}\},\{y(x)\to 2\sqrt{e^{c_1}x+e^{2c_1}}+e^{c_1}\}\}$$

✓ Maple : cpu = 0.464 (sec), leaf count = 119

$$\{\ln \left(x\right)-\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{y\left(x\right)+2x}{2x}\frac{1}{\sqrt{\frac{{\left(y\left(x\right)\right)}^2+xy\left(x\right)+x^2}{x^2}}}\right)+\ln \left(\frac{y\left(x\right)}{x}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,\ln \left(x\right)+\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{y\left(x\right)+2x}{2x}\frac{1}{\sqrt{\frac{{\left(y\left(x\right)\right)}^2+xy\left(x\right)+x^2}{x^2}}}\right)+\ln \left(\frac{y\left(x\right)}{x}\right)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=(-\frac{1}{2}-\frac{i}{2}\sqrt{3})x,y\left(x\right)=(-\frac{1}{2}+\frac{i}{2}\sqrt{3})x\}$$