\[ y''(x)=\frac {3 y(x)}{4 \left (x^2+x+1\right )^2} \] ✓ Mathematica : cpu = 0.024178 (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 = 0.022 (sec), leaf count = 28
\[y \relax (x ) = \sqrt {x^{2}+x +1}\, \left (\arctan \left (\frac {\left (2 x +1\right ) \sqrt {3}}{3}\right ) c_{2}+c_{1}\right )\]