\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =18\,{\frac {y \left ( x \right ) }{ \left ( 2\,x+1 \right ) ^{2} \left ( {x}^{2}+x+1 \right ) }}=0} \]
Mathematica: cpu = 0.089011 (sec), leaf count = 108 \[ \left \{\left \{y(x)\to \frac {c_1 \left (x^2+x+1\right )}{(2 x+1)^2}+\frac {c_2 \left (16 x^3+24 x^2-12 \sqrt {3} x^2 \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )+30 x-12 \sqrt {3} x \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )-12 \sqrt {3} \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )+11\right )}{(2 x+1)^2}\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 68 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{2}+x+1 \right ) }{ \left ( 2\,x+1 \right ) ^{2}}}+{\frac {{\it \_C2}}{ \left ( 2 \,x+1 \right ) ^{2}} \left ( \left ( 36\,{x}^{2}+36\,x+36 \right ) \arctan \left ( {\frac { \left ( 2\,x+1 \right ) \sqrt {3}}{3}} \right ) - 16\,\sqrt {3} \left ( {x}^{3}+{x}^{2}+{\frac {11\,x}{8}}+3/16 \right ) \right ) } \right \} \]