3.397   ODE No. 397

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-2x^3{\left(y\left(x\right)\right)}^2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-4x^2{\left(y\left(x\right)\right)}^3=0}}$$

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

Mathematica: cpu = 0.431555 (sec), leaf count = 143 $$\{\text{Solve}[-\frac{x\sqrt{x^{4}y(x)+4}y(x{)}^{3/2}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{2\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}}-\frac{1}{4}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{xy(x{)}^{3/2}\sqrt{x^{4}y(x)+4}{\sinh }^{-1}\left(\frac{1}{2}{x}^2\sqrt{y(x)}\right)}{2\sqrt{x^{2}y(x{)}^3(x^{4}y(x)+4)}}-\frac{1}{4}\log (y(x))=c_1,y(x)]\}$$

Maple: cpu = 0.671 (sec), leaf count = 131 $$\{y\left(x\right)=-4x^{-4},y\left(x\right)=\frac{(\sqrt{2}{x}^2\mathit{\_}\mathit{C}\mathit{1}-2){\mathit{\_}\mathit{C}\mathit{1}}^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^4-4},y\left(x\right)=-\frac{(\sqrt{2}{x}^2\mathit{\_}\mathit{C}\mathit{1}+2){\mathit{\_}\mathit{C}\mathit{1}}^2}{2{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^4-4},y\left(x\right)=-2\frac{\sqrt{2}{x}^2\mathit{\_}\mathit{C}\mathit{1}-{\mathit{\_}\mathit{C}\mathit{1}}^2}{{\mathit{\_}\mathit{C}\mathit{1}}^2(-2x^4+{\mathit{\_}\mathit{C}\mathit{1}}^2)},y\left(x\right)=2\frac{\sqrt{2}{x}^2\mathit{\_}\mathit{C}\mathit{1}+{\mathit{\_}\mathit{C}\mathit{1}}^2}{{\mathit{\_}\mathit{C}\mathit{1}}^2(-2x^4+{\mathit{\_}\mathit{C}\mathit{1}}^2)}\}$$