\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =- \left ( {\frac {{\it Ei} \left ( 1,-\ln \left ( -1+y \left ( x \right ) \right ) \right ) }{x}}-{\it \_F1} \left ( x \right ) \right ) \ln \left ( -1+y \left ( x \right ) \right ) =0} \]
Mathematica: cpu = 1.114141 (sec), leaf count = 32 \[ \text {DSolve}\left [y'(x)=\log (y(x)-1) \left (\text {$\_$F1}(x)-\frac {\text {Ei}(-\log (y(x)-1))}{x}\right ),y(x),x\right ] \]
Maple: cpu = 0.172 (sec), leaf count = 27 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( \int \!{ \frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}xx+x{\it \_C1}+{\it Ei} \left ( 1,-{\it \_Z} \right ) \right ) }}+1 \right \} \]