\[ y'(x)=\frac {y(x) \left (\text {$\_$F1}(x)+\frac {\log ^2(y(x))}{2 x}\right )}{\log (y(x))} \] ✓ Mathematica : cpu = 0.312793 (sec), leaf count = 80
\[\text {Solve}\left [\int _1^x\left (-\frac {\log ^2(y(x))}{2 K[1]^2}-\frac {\text {$\_$F1}(K[1])}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (\frac {\log (K[2])}{x K[2]}-\int _1^x-\frac {\log (K[2])}{K[1]^2 K[2]}dK[1]\right )dK[2]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.128 (sec), leaf count = 46
\[\left \{y \left (x \right ) = {\mathrm e}^{\sqrt {2 c_{1} x +2 x \left (\int \frac {\textit {\_F1} \left (x \right )}{x}d x \right )}}, y \left (x \right ) = {\mathrm e}^{-\sqrt {2}\, \sqrt {\left (c_{1}+\int \frac {\textit {\_F1} \left (x \right )}{x}d x \right ) x}}\right \}\]