2.508   ODE No. 508

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

$$(x^{2}y(x{)}^2-x^2+y(x{)}^4)y^{\prime }(x{)}^2+2xy(x)y^{\prime }(x)-y(x{)}^2=0$$ ✓ Mathematica : cpu = 2.07293 (sec), leaf count = 88

$$\text{Solve}[\frac{\sqrt{x^2+y(x{)}^2}y(x)(\log (\frac{x}{\sqrt{x^2+y(x{)}^2}}+1)-\log (1-\frac{x}{\sqrt{x^2+y(x{)}^2}}))}{2x^2\sqrt{\frac{y(x{)}^2(x^2+y(x{)}^2)}{x^4}}}+y(x)=c_1,y(x)]$$ ✓ Maple : cpu = 3.458 (sec), leaf count = 60

$$\{y\left(x\right)=-ix,y\left(x\right)=ix,y\left(x\right)=-\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\left(\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{\_}\mathit{Z}\right)\right)}^2{\mathit{\_}\mathit{Z}}^2-2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+{\mathit{\_}\mathit{Z}}^2{x}^2-x^2)\right)+\mathit{\_}\mathit{C}\mathit{1}\}$$