\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {2\,F \left( y \left( x \right) +\ln  \left( 2\,x+1 \right)  \right) x+F \left( y \left( x \right) +\ln  \left( 2\,x+1 \right)  \right) -2}{2\,x+1}}=0}
\]