\[ y''(x)=\frac {3 y(x)}{4 \left (x^2+x+1\right )^2} \] ✓ Mathematica : cpu = 0.025761 (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 = 0.049 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =\sqrt {{x}^{2}+x+1} \left ( \arctan \left ( {\frac { \left ( 2\,x+1 \right ) \sqrt {3}}{3}} \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \]