3.220   ODE No. 220

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

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

Mathematica: cpu = 0.012002 (sec), leaf count = 57 $$\{\{y(x)\to -\sqrt{c_1{e}^{\frac{x^2}{2}}-x^2-2}\},\{y(x)\to \sqrt{c_1{e}^{\frac{x^2}{2}}-x^2-2}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 43 $$\{y\left(x\right)=\sqrt{{\mathrm{e}}^{\frac{x^2}{2}}\mathit{\_}\mathit{C}\mathit{1}-x^2-2},y\left(x\right)=-\sqrt{{\mathrm{e}}^{\frac{x^2}{2}}\mathit{\_}\mathit{C}\mathit{1}-x^2-2}\}$$