\[ y(x) (x F(0,2)+x F(2,0)) y''(x)+x F(2,2) y''(x)^2+x F(1,1) y''(x)+y'(x) \left ((x F(1,2)+x F(2,1)) y''(x)+y(x) (x F(0,1)+x F(1,0))\right )+x F(0,0) y(x)^2=0 \] ✗ Mathematica : cpu = 506.625 (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 = 1.238 (sec), leaf count = 163
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{2\, \left ( F_{{2,2}} \right ) \left ( {\it \_a} \right ) } \left ( \sqrt { \left ( \left ( \left ( F_{{2,1}} \right ) \left ( {\it \_a} \right ) \right ) ^{2}+2\, \left ( F_{{1,2}} \right ) \left ( {\it \_a} \right ) \left ( F_{{2,1}} \right ) \left ( {\it \_a} \right ) -4\, \left ( F_{{2,2}} \right ) \left ( {\it \_a} \right ) \left ( F_{{1,1}} \right ) \left ( {\it \_a} \right ) + \left ( \left ( F_{{1,2}} \right ) \left ( {\it \_a} \right ) \right ) ^{2} \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+ \left ( \left ( 2\, \left ( F_{{0,2}} \right ) \left ( {\it \_a} \right ) +2\, \left ( F_{{2,0}} \right ) \left ( {\it \_a} \right ) \right ) \left ( F_{{1,2}} \right ) \left ( {\it \_a} \right ) + \left ( 2\, \left ( F_{{0,2}} \right ) \left ( {\it \_a} \right ) +2\, \left ( F_{{2,0}} \right ) \left ( {\it \_a} \right ) \right ) \left ( F_{{2,1}} \right ) \left ( {\it \_a} \right ) -4\, \left ( F_{{2,2}} \right ) \left ( {\it \_a} \right ) \left ( \left ( F_{{0,1}} \right ) \left ( {\it \_a} \right ) + \left ( F_{{1,0}} \right ) \left ( {\it \_a} \right ) \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) -4\, \left ( F_{{2,2}} \right ) \left ( {\it \_a} \right ) \left ( F_{{0,0}} \right ) \left ( {\it \_a} \right ) + \left ( \left ( F_{{0,2}} \right ) \left ( {\it \_a} \right ) + \left ( F_{{2,0}} \right ) \left ( {\it \_a} \right ) \right ) ^{2}}-2\, \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \left ( F_{{2,2}} \right ) \left ( {\it \_a} \right ) + \left ( - \left ( F_{{2,1}} \right ) \left ( {\it \_a} \right ) - \left ( F_{{1,2}} \right ) \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) - \left ( F_{{0,2}} \right ) \left ( {\it \_a} \right ) - \left ( F_{{2,0}} \right ) \left ( {\it \_a} \right ) \right ) } \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]