\[ y''(x)=-\frac {f'(x) y'(x)}{2 f(x)}-\frac {g(x) y(x)}{f(x)} \] ✗ Mathematica : cpu = 0.280032 (sec), leaf count = 0 , could not solve
DSolve[Derivative[2][y][x] == -((g[x]*y[x])/f[x]) - (Derivative[1][f][x]*Derivative[1][y][x])/(2*f[x]), y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {g \left ( x \right ) {\it \_Y} \left ( x \right ) }{f \left ( x \right ) }}+{\frac { \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) }{2\,f \left ( x \right ) }}+{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]