\[ y(x) \left (a+f'(x)\right )+f(x) y'(x)-g(x)+y''(x)=0 \] ✗ Mathematica : cpu = 0.206154 (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 or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \relax (x )+f \relax (x ) \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )+\left (\frac {d}{d x}f \relax (x )+a \right ) \textit {\_Y} \relax (x )-g \relax (x )\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]