\[ a y'(x)^2+f(x) y(x) y'(x)+g(x) y(x)^2+y(x) y''(x)=0 \] ✗ Mathematica : cpu = 42.7746 (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
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left ({\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (-a -1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}-\textit {\_}b\left (\textit {\_a} \right ) f \left (\textit {\_a} \right )-g \left (\textit {\_a} \right )\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=\frac {\frac {d}{d x}y \left (x \right )}{y \left (x \right )}\right \}, \left \{x =\textit {\_a} , y \left (x \right )={\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]