8.228   ODE No. 1818

$$\boxed{{\displaystyle (x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-{({\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+1)}^2=0}}$$

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

Mathematica: cpu = 1.402678 (sec), leaf count = 35 $$\text{DSolve}[(x{y}^{\prime }(x)-y(x))y^{″}(x)-{(y^{\prime }(x{)}^2+1)}^2=0,y(x),x]$$

Maple: cpu = 0.265 (sec), leaf count = 66 $$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{-\mathit{\_}\mathit{f}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}+\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)+\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)\mathit{\_}\mathit{Z}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{f}+\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)+\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}-\mathit{\_}\mathit{f})}{{\mathit{\_}\mathit{f}}^2+1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2})x\}$$