\[ y'(x)=\frac {y(x)}{x \log (x)}-F(x) \left (-y(x)^2-2 y(x) \log (x)-\log ^2(x)\right ) \] ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.049 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-{\frac {\ln \left ( x \right ) \left ( \int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}-2 \right ) }{\int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}}} \right \} \]