\[ -f(x)+x^2 y^{(3)}(x)+x y''(x)+(2 x y(x)-1) y'(x)+y(x)^2=0 \] ✗ Mathematica : cpu = 0.103107 (sec), leaf count = 0
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]
, 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. (sec), leaf count = 0
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+x*diff(diff(y(x),x),x)+(2*x*y(x)-1)*diff(y(x),x)+y(x)^2-f(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \textit {\_}b\left (\textit {\_a} \right )\boldsymbol {\mathrm {where}}\left [\left \{\textit {\_a}^{2} \left (\frac {d^{2}}{d \textit {\_a}^{2}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )+\textit {\_a} \textit {\_}b\left (\textit {\_a} \right )^{2}-\textit {\_a} \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-\left (\int f \left (\textit {\_a} \right )d \textit {\_a} \right )+c_{1}=0\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=y \left (x \right )\right \}, \left \{x =\textit {\_a} , y \left (x \right )=\textit {\_}b\left (\textit {\_a} \right )\right \}\right ]\]