\[ y'(x) \left (y(x)-\frac {3 f'(x)}{2 f(x)}\right )-\frac {y(x)^2 f'(x)}{2 f(x)}+y(x) \left (-\frac {f''(x)}{2 f(x)}+\frac {f'(x)^2}{f(x)^2}+f(x)\right )+y''(x)-y(x)^3=0 \] ✗ Mathematica : cpu = 1.06568 (sec), leaf count = 0 , could not solve
DSolve[-y[x]^3 - (y[x]^2*Derivative[1][f][x])/(2*f[x]) + (y[x] - (3*Derivative[1][f][x])/(2*f[x]))*Derivative[1][y][x] + y[x]*(f[x] + Derivative[1][f][x]^2/f[x]^2 - Derivative[2][f][x]/(2*f[x])) + Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve(diff(diff(y(x),x),x)+(y(x)-3/2*diff(f(x),x)/f(x))*diff(y(x),x)-y(x)^3-1/2*diff(f(x),x)/f(x)*y(x)^2+1/2*(f(x)+diff(f(x),x)^2/f(x)^2-diff(diff(f(x),x),x))/f(x)*y(x)=0,y(x))