2.466   ODE No. 466

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

$$y(x)y^{\prime }(x{)}^2-2x{y}^{\prime }(x)+y(x)=0$$ ✓ Mathematica : cpu = 1.78653 (sec), leaf count = 433

$$\{\text{Solve}[-\frac{i\sqrt{\frac{y(x{)}^2}{x^2}-1}{\tan }^{-1}\left(\sqrt{\frac{y(x{)}^2}{x^2}-1}\right)}{\sqrt{\frac{y(x)}{x}-1}\sqrt{\frac{y(x)}{x}+1}}-i\sqrt{\frac{\frac{y(x)}{x}-1}{\frac{y(x)}{x}+1}}(\frac{y(x)}{x}+1)+i\sqrt{\frac{y(x)}{x}-1}\sqrt{\frac{y(x)}{x}+1}+\log \left(\frac{y(x)}{x}\right)+\frac{2i\sqrt{\frac{y(x)}{x}-1}{\sin }^{-1}\left(\frac{\sqrt{1-\frac{y(x)}{x}}}{\sqrt{2}}\right)}{\sqrt{1-\frac{y(x)}{x}}}-2i{\tanh }^{-1}\left(\sqrt{\frac{\frac{y(x)}{x}-1}{\frac{y(x)}{x}+1}}\right)=-\log (x)+c_1,y(x)],\text{Solve}[\frac{i\sqrt{\frac{y(x{)}^2}{x^2}-1}{\tan }^{-1}\left(\sqrt{\frac{y(x{)}^2}{x^2}-1}\right)}{\sqrt{\frac{y(x)}{x}-1}\sqrt{\frac{y(x)}{x}+1}}+i\sqrt{\frac{\frac{y(x)}{x}-1}{\frac{y(x)}{x}+1}}(\frac{y(x)}{x}+1)-i\sqrt{\frac{y(x)}{x}-1}\sqrt{\frac{y(x)}{x}+1}+\log \left(\frac{y(x)}{x}\right)-\frac{2i\sqrt{\frac{y(x)}{x}-1}{\sin }^{-1}\left(\frac{\sqrt{1-\frac{y(x)}{x}}}{\sqrt{2}}\right)}{\sqrt{1-\frac{y(x)}{x}}}+2i{\tanh }^{-1}\left(\sqrt{\frac{\frac{y(x)}{x}-1}{\frac{y(x)}{x}+1}}\right)=-\log (x)+c_1,y(x)]\}$$ ✓ Maple : cpu = 1.161 (sec), leaf count = 71

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