\[ y''(x)=\frac {3 y(x)}{4 \left (x^2+x+1\right )^2} \] ✓ Mathematica : cpu = 0.0395254 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \frac {1}{3} \sqrt {x^2+x+1} \left (2 \sqrt {3} c_2 \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )+3 c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.039 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+x+1} \left ( \arctan \left ( {\frac { \left ( 2\,x+1 \right ) \sqrt {3}}{3}} \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \]