2.260   ODE No. 260

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

$$(2x^{2}y(x)+x)y^{\prime }(x)-x^{2}y(x{)}^3+2xy(x{)}^2+y(x)=0$$ ✓ Mathematica : cpu = 0.0148652 (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 = 0.033 (sec), leaf count = 59

$$\{y\left(x\right)=\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(-2+\sqrt{4-2\ln \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}}),y\left(x\right)=-\frac{1}{(2\ln \left(x\right)-2\mathit{\_}\mathit{C}\mathit{1})x}(2+\sqrt{4-2\ln \left(x\right)+2\mathit{\_}\mathit{C}\mathit{1}})\}$$