3.260   ODE No. 260

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

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

Mathematica: cpu = 0.012502 (sec), leaf count = 80 $$\{\{y(x)\to \frac{x}{\frac{\sqrt{x(c_1-2\log (x))+4x}}{\sqrt{\frac{1}{x^3}}}-2x^2}\},\{y(x)\to -\frac{x}{\frac{\sqrt{x(c_1-2\log (x))+4x}}{\sqrt{\frac{1}{x^3}}}+2x^2}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 59 $$\{y\left(x\right)=\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(-2+\sqrt{4-2\ln \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}}),y\left(x\right)=-\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(2+\sqrt{4-2\ln \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}})\}$$