\[ -f(x)+x^2 y^{(3)}(x)+(2 x y(x)-1) y'(x)+x y''(x)+y(x)^2=0 \] ✗ Mathematica : cpu = 0.0763858 (sec), leaf count = 0 , could not solve
DSolve[-f[x] + y[x]^2 + (-1 + 2*x*y[x])*Derivative[1][y][x] + x*Derivative[2][y][x] + x^2*Derivative[3][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.731 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ {{\it \_a}}^{2}{\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b} \left ( {\it \_a} \right ) +{\it \_a}\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-{\it \_a}\,{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -\int \!f \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \]