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 = 0.39306 (sec), leaf count = 269

$$\{\{y(x)\to -\frac{2\sqrt{-\sqrt{3}x\sinh (c_1)-\sqrt{3}x\cosh (c_1)+\sinh (2c_1)+\cosh (2c_1)}}{\sqrt{3}}-\frac{\sinh (c_1)}{\sqrt{3}}-\frac{\cosh (c_1)}{\sqrt{3}}\},\{y(x)\to \frac{2\sqrt{-\sqrt{3}x\sinh (c_1)-\sqrt{3}x\cosh (c_1)+\sinh (2c_1)+\cosh (2c_1)}}{\sqrt{3}}-\frac{\sinh (c_1)}{\sqrt{3}}-\frac{\cosh (c_1)}{\sqrt{3}}\},\{y(x)\to -\frac{2\sqrt{\sqrt{3}x\sinh (c_1)+\sqrt{3}x\cosh (c_1)+\sinh (2c_1)+\cosh (2c_1)}}{\sqrt{3}}+\frac{\sinh (c_1)}{\sqrt{3}}+\frac{\cosh (c_1)}{\sqrt{3}}\},\{y(x)\to \frac{2\sqrt{\sqrt{3}x\sinh (c_1)+\sqrt{3}x\cosh (c_1)+\sinh (2c_1)+\cosh (2c_1)}}{\sqrt{3}}+\frac{\sinh (c_1)}{\sqrt{3}}+\frac{\cosh (c_1)}{\sqrt{3}}\}\}$$ ✓ Maple : cpu = 1.371 (sec), leaf count = 121

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