\[ \left (x y'(x)-y(x)\right ) y''(x)-\left (y'(x)^2+1\right )^2=0 \] ✗ Mathematica : cpu = 0.897119 (sec), leaf count = 0
DSolve[-(1 + Derivative[1][y][x]^2)^2 + (-y[x] + x*Derivative[1][y][x])*Derivative[2][y][x] == 0,y[x],x]
, 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 = 0.398 (sec), leaf count = 66
dsolve((x*diff(y(x),x)-y(x))*diff(diff(y(x),x),x)-(diff(y(x),x)^2+1)^2=0,y(x))
\[y \left (x \right ) = \RootOf \left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}\frac {-\textit {\_f} +\RootOf \left (-c_{1} \tan \left (\frac {1}{\textit {\_Z}}\right ) \textit {\_Z} +\textit {\_f} c_{1} \tan \left (\frac {1}{\textit {\_Z}}\right )+c_{1} \textit {\_Z} \textit {\_f} +\tan \left (\frac {1}{\textit {\_Z}}\right ) \textit {\_Z} \textit {\_f} +c_{1}+\tan \left (\frac {1}{\textit {\_Z}}\right )+\textit {\_Z} -\textit {\_f} \right )}{\textit {\_f}^{2}+1}d \textit {\_f} +c_{2}\right ) x\]