3.508   ODE No. 508

$$\boxed{{\displaystyle ({\left(y\left(x\right)\right)}^4+x^2{\left(y\left(x\right)\right)}^2-x^2){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+2xy\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 55.171506 (sec), leaf count = 47 $$\text{DSolve}[(x^{2}y(x{)}^2-x^2+y(x{)}^4)y^{\prime }(x{)}^2+2xy(x)y^{\prime }(x)-y(x{)}^2=0,y(x),x]$$

Maple: cpu = 2.122 (sec), leaf count = 60 $$\{y\left(x\right)=-ix,y\left(x\right)=ix,y\left(x\right)=-\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\left(\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{\_}\mathit{Z}\right)\right)}^2{\mathit{\_}\mathit{Z}}^2-2\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{Z}}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+{\mathit{\_}\mathit{Z}}^2{x}^2-x^2)\right)+\mathit{\_}\mathit{C}\mathit{1}\}$$