\[ y'(x)=\frac {y(x)}{x \log (x)}-F(x) \left (-y(x)^2-2 y(x) \log (x)-\log ^2(x)\right ) \] ✓ Mathematica : cpu = 1.43647 (sec), leaf count = 73
\[\left \{\left \{y(x)\to \frac {\int _1^x\frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}}dK[5]-1+c_1}{\sqrt {\frac {1}{\log ^2(x)}} \int _1^x\frac {F(K[5])}{\sqrt {\frac {1}{\log ^2(K[5])}}}dK[5]+c_1 \sqrt {\frac {1}{\log ^2(x)}}}\right \}\right \}\] ✓ Maple : cpu = 0.164 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-{\frac {\ln \left ( x \right ) \left ( \int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}-2 \right ) }{\int \!-2\,\ln \left ( x \right ) F \left ( x \right ) \,{\rm d}x-{\it \_C1}}} \right \} \]