3.254   ODE No. 254

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

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

Mathematica: cpu = 0.030004 (sec), leaf count = 99 $$\{\{y(x)\to -\frac{2x}{\frac{\sqrt{2}\sqrt{-2x(c_1-\log (x))-\frac{x}{2}}}{\sqrt{-\frac{1}{x^3}}}-x^2}\},\{y(x)\to \frac{2x}{\frac{\sqrt{2}\sqrt{-2x(c_1-\log (x))-\frac{x}{2}}}{\sqrt{-\frac{1}{x^3}}}+x^2}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 59 $$\{y\left(x\right)=-\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(-1+\sqrt{1-4\ln \left(x\right)+4\mathit{\_}\mathit{C}\mathit{1}}),y\left(x\right)=\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(1+\sqrt{1-4\ln \left(x\right)+4\mathit{\_}\mathit{C}\mathit{1}})\}$$