2.254   ODE No. 254

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

$$x^{2}y(x{)}^3+x(xy(x)-2)y^{\prime }(x)+xy(x{)}^2-2y(x)=0$$ ✓ Mathematica : cpu = 0.123539 (sec), leaf count = 99

$$\{\{y(x)\to -\frac{2x}{-x^2+\frac{\sqrt{2}\sqrt{-\frac{x}{2}-2x(-\log (x)+c_1)}}{\sqrt{-\frac{1}{x^3}}}}\},\{y(x)\to \frac{2x}{x^2+\frac{\sqrt{2}\sqrt{-\frac{x}{2}-2x(-\log (x)+c_1)}}{\sqrt{-\frac{1}{x^3}}}}\}\}$$ ✓ Maple : cpu = 0.022 (sec), leaf count = 59

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