3.466   ODE No. 466

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

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

Mathematica: cpu = 0.248532 (sec), leaf count = 145 $$\{\{y(x)\to -\sqrt{-2x\sinh \left(c_1\right)-2x\cosh \left(c_1\right)-\sinh \left(2c_1\right)-\cosh \left(2c_1\right)}\},\{y(x)\to \sqrt{-2x\sinh \left(c_1\right)-2x\cosh \left(c_1\right)-\sinh \left(2c_1\right)-\cosh \left(2c_1\right)}\},\{y(x)\to -\sqrt{2x\sinh \left(c_1\right)+2x\cosh \left(c_1\right)-\sinh \left(2c_1\right)-\cosh \left(2c_1\right)}\},\{y(x)\to \sqrt{2x\sinh \left(c_1\right)+2x\cosh \left(c_1\right)-\sinh \left(2c_1\right)-\cosh \left(2c_1\right)}\}\}$$

Maple: cpu = 0.811 (sec), leaf count = 71 $$\{y\left(x\right)=x,y\left(x\right)=\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-2ix\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+2ix\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=-x,y\left(x\right)=-\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2-2ix\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=-\sqrt{{\mathit{\_}\mathit{C}\mathit{1}}^2+2ix\mathit{\_}\mathit{C}\mathit{1}}\}$$