\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =3/4\,{\frac {y \left ( x \right ) }{ \left ( {x}^{2}+x+1 \right ) ^{2}}}=0} \]
Mathematica: cpu = 0.038505 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to c_1 \sqrt {x^2+x+1}+\frac {2 c_2 \sqrt {x^2+x+1} \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )}{\sqrt {3}}\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {{x}^{2}+x+1}+{\it \_C2 }\,\arctan \left ( {\frac { \left ( 2\,x+1 \right ) \sqrt {3}}{3}} \right ) \sqrt {{x}^{2}+x+1} \right \} \]