\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) =-F \left( x \right)  \left( - \left( y \left( x \right)  \right) ^{2}-2\,y \left( x \right) \ln  \left( x \right) - \left( \ln  \left( x \right)  \right) ^{2} \right) +{\frac {y \left( x \right) }{x\ln  \left( x \right) }}=0}
\]