\[ y(x) \left (a+f'(x)\right )+f(x) y'(x)-g(x)+y''(x)=0 \] ✗ Mathematica : cpu = 0.206154 (sec), leaf count = 0
DSolve[-g[x] + y[x]*(a + Derivative[1][f][x]) + f[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
, 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
dsolve(diff(diff(y(x),x),x)+f(x)*diff(y(x),x)+(diff(f(x),x)+a)*y(x)-g(x)=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )+f \left (x \right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )+\left (\frac {d}{d x}f \left (x \right )+a \right ) \textit {\_Y} \left (x \right )-g \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]