\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {2\,x \left( y \left( x \right)  \right) ^{2}+4\,y \left( x \right) \ln  \left( 2\,x+1 \right) x+2\, \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}x+ \left( y \left( x \right)  \right) ^{2}-2+ \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}+2\,y \left( x \right) \ln  \left( 2\,x+1 \right) }{2\,x+1}}=0}
\]