2.1818   ODE No. 1818

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

$$(x{y}^{\prime }(x)-y(x))y^{″}(x)-{(y^{\prime }(x{)}^2+1)}^2=0$$ ✗ Mathematica : cpu = 1.47361 (sec), leaf count = 0 , could not solve

DSolve[-(1 + Derivative[1][y][x]^2)^2 + (-y[x] + x*Derivative[1][y][x])*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.75 (sec), leaf count = 66

$$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{-\mathit{\_}\mathit{f}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{C}\mathit{1}\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)\mathit{\_}\mathit{Z}+\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{f}+\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)\mathit{\_}\mathit{Z}\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1}+\tan \left({\mathit{\_}\mathit{Z}}^{-1}\right)+\mathit{\_}\mathit{Z}-\mathit{\_}\mathit{f})}{{\mathit{\_}\mathit{f}}^2+1}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2})x\}$$