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 = 0.114147 (sec), leaf count = 80

$$\{\{y(x)\to \frac{x}{-2x^2+\frac{\sqrt{4x+x(-2\log (x)+c_1)}}{\sqrt{\frac{1}{x^3}}}}\},\{y(x)\to -\frac{x}{2x^2+\frac{\sqrt{4x+x(-2\log (x)+c_1)}}{\sqrt{\frac{1}{x^3}}}}\}\}$$ ✓ Maple : cpu = 0.023 (sec), leaf count = 59

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