\[ y'(x)=\frac {y(x)}{x \log (x)}-F(x) \left (-y(x)^2-2 y(x) \log (x)-\log ^2(x)\right ) \] ✓ Mathematica : cpu = 1.40908 (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 = 0.034 (sec), leaf count = 35
\[y \relax (x ) = -\frac {\ln \relax (x ) \left (\int -2 F \relax (x ) \ln \relax (x )d x -c_{1}-2\right )}{\int -2 F \relax (x ) \ln \relax (x )d x -c_{1}}\]