\[ y'(x)=\frac {y(x)}{x \log (x)}-F(x) \left (-y(x)^2-2 y(x) \log (x)-\log ^2(x)\right ) \] ✓ Mathematica : cpu = 455.437 (sec), leaf count = 71
\[\left \{\left \{y(x)\to \frac {\int _1^x \frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}} \, dK[5]+c_1-1}{\sqrt {\frac {1}{\log ^2(x)}} \left (\int _1^x \frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}} \, dK[5]\right )+c_1 \sqrt {\frac {1}{\log ^2(x)}}}\right \}\right \}\]
✓ Maple : cpu = 0.027 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-{\frac {\ln \left ( x \right ) \left ( \int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}-2 \right ) }{\int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}}} \right \} \]