\[ a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 42.0878 (sec), leaf count = 0 , could not solve
DSolve[g[x]*y[x]^2 + f[x]*y[x]*Derivative[1][y][x] + a*Derivative[1][y][x]^2 + y[x]*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.628 (sec), leaf count = 70
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( -a-1 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}-f \left ( {\it \_a} \right ) {\it \_b} \left ( {\it \_a} \right ) -g \left ( {\it \_a} \right ) \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{y \left ( x \right ) }} \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]