2.505   ODE No. 505

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

$$-x^3+xy(x{)}^2{y}^{\prime }(x{)}^2-2y(x{)}^3{y}^{\prime }(x)+2xy(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0126403 (sec), leaf count = 73

$$\{\{y(x)\to -\sqrt{2c_1+x^2}\},\{y(x)\to \sqrt{2c_1+x^2}\},\{y(x)\to -\sqrt{c_1{x}^4+x^2}\},\{y(x)\to \sqrt{c_1{x}^4+x^2}\}\}$$

✓ Maple : cpu = 0.033 (sec), leaf count = 52

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