\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac {y \left ( x \right ) }{\ln \left ( y \left ( x \right ) \right ) } \left ( -1/2\,{\frac { \left ( \ln \left ( y \left ( x \right ) \right ) \right ) ^{2}}{x}}-{\it \_F1} \left ( x \right ) \right ) }=0} \]
Mathematica: cpu = 0.800602 (sec), leaf count = 55 \[ \text {Solve}\left [\text {ConditionalExpression}\left [\int _1^x \left (-\frac {\text {$\_$F1}(K[1])}{K[1]}-\frac {\log ^2(y(x))}{2 K[1]^2}\right ) \, dK[1]+\frac {1}{2} \log ^2(y(x))=c_1,\Re (x)>0\lor x\notin \mathbb {R}\right ],y(x)\right ] \]
Maple: cpu = 0.094 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {2\,\int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}xx+2\,x{\it \_C1}}}},y \left ( x \right ) ={{\rm e}^{-\sqrt {2\,\int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}xx+2\,x{\it \_C1}}}} \right \} \]