\[ y(x) (x F(0,2)+x F(2,0)) y''(x)+x F(2,2) y''(x)^2+x F(1,1) y''(x)+y'(x) \left ((x F(1,2)+x F(2,1)) y''(x)+y(x) (x F(0,1)+x F(1,0))\right )+x F(0,0) y(x)^2=0 \] ✗ Mathematica : cpu = 78.6372 (sec), leaf count = 0 , could not solve
DSolve[x*F[0, 0]*y[x]^2 + x*F[1, 1]*Derivative[2][y][x] + (x*F[0, 2] + x*F[2, 0])*y[x]*Derivative[2][y][x] + x*F[2, 2]*Derivative[2][y][x]^2 + Derivative[1][y][x]*((x*F[0, 1] + x*F[1, 0])*y[x] + (x*F[1, 2] + x*F[2, 1])*Derivative[2][y][x]) == 0, y[x], x]
✓ Maple : cpu = 1.721 (sec), leaf count = 163
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left ({\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {-2 \textit {\_}b\left (\textit {\_a} \right )^{2} F_{2,2}\left (\textit {\_a} \right )+\left (-F_{1,2}\left (\textit {\_a} \right )-F_{2,1}\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )-F_{0,2}\left (\textit {\_a} \right )-F_{2,0}\left (\textit {\_a} \right )+\sqrt {\left (-4 F_{1,1}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right )+F_{1,2}\left (\textit {\_a} \right )^{2}+2 F_{1,2}\left (\textit {\_a} \right ) F_{2,1}\left (\textit {\_a} \right )+F_{2,1}\left (\textit {\_a} \right )^{2}\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}-4 F_{0,0}\left (\textit {\_a} \right ) F_{2,2}\left (\textit {\_a} \right )+\left (\left (2 F_{0,2}\left (\textit {\_a} \right )+2 F_{2,0}\left (\textit {\_a} \right )\right ) F_{1,2}\left (\textit {\_a} \right )+\left (2 F_{0,2}\left (\textit {\_a} \right )+2 F_{2,0}\left (\textit {\_a} \right )\right ) F_{2,1}\left (\textit {\_a} \right )-4 \left (F_{0,1}\left (\textit {\_a} \right )+F_{1,0}\left (\textit {\_a} \right )\right ) F_{2,2}\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )+\left (F_{0,2}\left (\textit {\_a} \right )+F_{2,0}\left (\textit {\_a} \right )\right )^{2}}}{2 F_{2,2}\left (\textit {\_a} \right )}\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=\frac {\frac {d}{d x}y \left (x \right )}{y \left (x \right )}\right \}, \left \{x =\textit {\_a} , y \left (x \right )={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]