\[ y'(x)=-\frac {y(x) \left (-\text {$\_$F1}(x)-\frac {\log ^2(y(x))}{2 x}\right )}{\log (y(x))} \] ✓ Mathematica : cpu = 1.05789 (sec), leaf count = 53
\[\text {Solve}\left [\text {ConditionalExpression}\left [2 c_1=2 \int _1^x -\frac {2 K[1] \text {$\_$F1}(K[1])+\log ^2(y(x))}{2 K[1]^2} \, dK[1]+\log ^2(y(x)),\Re (x)>0\lor x\notin \mathbb {R}\right ],y(x)\right ]\]
✓ Maple : cpu = 0.154 (sec), leaf count = 46
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {2\,\int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}xx+2\,{\it \_C1}\,x}}},y \left ( x \right ) ={{\rm e}^{-\sqrt {2}\sqrt {x \left ( \int \!{\frac {{\it \_F1} \left ( x \right ) }{x}}\,{\rm d}x+{\it \_C1} \right ) }}} \right \} \]