\[ y'(x)=-\frac {y(x) \left (-\text {$\_$F1}(x)-\frac {\log ^2(y(x))}{2 x}\right )}{\log (y(x))} \] ✓ Mathematica : cpu = 0.892876 (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 = 0.201 (sec), leaf count = 46
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {2\,\int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}xx+2\,{\it \_C1}\,x}}},y \left ( x \right ) ={{\rm e}^{-\sqrt {2}\sqrt {x \left ( \int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}x+{\it \_C1} \right ) }}} \right \} \]