3.400   ODE No. 400

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.624 (sec), leaf count = 123 $$\{y\left(x\right)=\frac{x^3}{6},y\left(x\right)=-\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}}(-\mathit{\_}\mathit{C}\mathit{1}{x}^3-x(-x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x})-3),y\left(x\right)=-\frac{1}{3\mathit{\_}\mathit{C}\mathit{1}}(-\mathit{\_}\mathit{C}\mathit{1}{x}^3+x(x^2\mathit{\_}\mathit{C}\mathit{1}+\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x})-3),y\left(x\right)=\frac{x^3}{3}+\frac{x}{3}(-x^2-\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x})+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{x^3}{3}+\frac{x}{3}(-x^2+\sqrt{-6\mathit{\_}\mathit{C}\mathit{1}x})+\mathit{\_}\mathit{C}\mathit{1}\}$$