\[ y'(x)=\log (y(x)-1) \left (\text {$\_$F1}(x)-\frac {\text {Ei}(-\log (y(x)-1))}{x}\right ) \] ✗ Mathematica : cpu = 0.684188 (sec), leaf count = 0
DSolve[Derivative[1][y][x] == Log[-1 + y[x]]*(-(ExpIntegralEi[-Log[-1 + y[x]]]/x) + _F1[x]),y[x],x]
, could not solve
DSolve[Derivative[1][y][x] == Log[-1 + y[x]]*(-(ExpIntegralEi[-Log[-1 + y[x]]]/x) + _F1[x]), y[x], x]
✓ Maple : cpu = 0.193 (sec), leaf count = 27
dsolve(diff(y(x),x) = -(1/x*Ei(1,-ln(-1+y(x)))-_F1(x))*ln(-1+y(x)),y(x))
\[y \left (x \right ) = {\mathrm e}^{\RootOf \left (\left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x \right ) x +x c_{1}+\Ei \left (1, -\textit {\_Z} \right )\right )}+1\]