3.505   ODE No. 505

$$\boxed{{\displaystyle x{\left(y\left(x\right)\right)}^2{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2{\left(y\left(x\right)\right)}^3\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2x{\left(y\left(x\right)\right)}^2-x^3=0}}$$

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

Mathematica: cpu = 0.013002 (sec), leaf count = 73 $$\{\{y(x)\to -\sqrt{2c_1+x^2}\},\{y(x)\to \sqrt{2c_1+x^2}\},\{y(x)\to -\sqrt{c_1{x}^4+x^2}\},\{y(x)\to \sqrt{c_1{x}^4+x^2}\}\}$$

Maple: cpu = 0.032 (sec), leaf count = 52 $$\{y\left(x\right)=\sqrt{x^2+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+1}x,y\left(x\right)=-\sqrt{x^2+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=-\sqrt{x^2\mathit{\_}\mathit{C}\mathit{1}+1}x\}$$