\[ y(x) \left (a+f'(x)\right )+f(x) y'(x)-g(x)+y''(x)=0 \] ✗ Mathematica : cpu = 0.20895 (sec), leaf count = 0 , could not solve
DSolve[-g[x] + y[x]*(a + Derivative[1][f][x]) + f[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +f \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) +a \right ) {\it \_Y} \left ( x \right ) -g \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]