\[ y''(x)=-\frac {f'(x) y'(x)}{2 f(x)}-\frac {g(x) y(x)}{f(x)} \] ✗ Mathematica : cpu = 0.297395 (sec), leaf count = 0
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]
, 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
dsolve(diff(diff(y(x),x),x) = -1/2*diff(f(x),x)*diff(y(x),x)/f(x)-g(x)/f(x)*y(x),y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {g \left (x \right ) \textit {\_Y} \left (x \right )}{f \left (x \right )}+\frac {\left (\frac {d}{d x}f \left (x \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{2 f \left (x \right )}+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]