\[
\boxed{
{\frac {\rm d}{{\rm d}x}}y \left( x \right) ={\frac {2\,x+4\,y \left( x \right) \ln  \left( 2\,x+1 \right) x+6\, \left( y \left( x \right)  \right) ^{2}\ln  \left( 2\,x+1 \right) x+6\,y \left( x \right)  \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}x+2\, \left( \ln  \left( 2\,x+1 \right)  \right) ^{3}x+2\,x \left( y \left( x \right)  \right) ^{3}+2\, \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}x+2\,x \left( y \left( x \right)  \right) ^{2}-1+3\, \left( y \left( x \right)  \right) ^{2}\ln  \left( 2\,x+1 \right) +3\,y \left( x \right)  \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}+ \left( y \left( x \right)  \right) ^{2}+ \left( y \left( x \right)  \right) ^{3}+2\,y \left( x \right) \ln  \left( 2\,x+1 \right) + \left( \ln  \left( 2\,x+1 \right)  \right) ^{2}+ \left( \ln  \left( 2\,x+1 \right)  \right) ^{3}}{2\,x+1}}=0}
\]