\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {-2\,y \left( x \right) -2\,\ln  \left( 2\,x+1 \right) -2+2\,x \left( y \left( x \right)  \right) ^{3}+ \left( y \left( x \right)  \right) ^{3}+6\, \left( y \left( x \right)  \right) ^{2}\ln  \left( 2\,x+1 \right) x+3\, \left( y \left( x \right)  \right) ^{2}\ln  \left( 2\,x+1 \right) +6\,y \left( x \right)  \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}x+3\,y \left( x \right)  \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}+2\, \left( \ln  \left( 2\,x+1 \right)  \right) ^{3}x+ \left( \ln  \left( 2\,x+1 \right)  \right) ^{3}}{ \left( 2\,x+1 \right)  \left( y \left( x \right) +\ln  \left( 2\,x+1 \right) +1 \right) }}=0}
\]