\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,x+4\,y \left ( x \right ) \ln \left ( 2\,x+1 \right ) x+6\, \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( 2\,x+1 \right ) x+6\,y \left ( x \right ) \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{2}x+2\, \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{3}x+2\,x \left ( y \left ( x \right ) \right ) ^{3}+2\, \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{2}x+2\,x \left ( y \left ( x \right ) \right ) ^{2}-1+3\, \left ( y \left ( x \right ) \right ) ^{2}\ln \left ( 2\,x+1 \right ) +3\,y \left ( x \right ) \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{3}+2\,y \left ( x \right ) \ln \left ( 2\,x+1 \right ) + \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{2}+ \left ( \ln \left ( 2\,x+1 \right ) \right ) ^{3}}{2\,x+1}}=0} \]
Mathematica: cpu = 0.060508 (sec), leaf count = 82 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 y(x)+3 \log (2 x+1)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) =-\ln \left ( 2\,x+1 \right ) -{\frac {1}{3 }}+{\frac {29\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841 \,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{ \it \_C1} \right ) }{9}} \right \} \]