\[ y''(x)=\frac {18 y(x)}{(2 x+1)^2 \left (x^2+x+1\right )} \] ✓ Mathematica : cpu = 0.0585625 (sec), leaf count = 108
DSolve[Derivative[2][y][x] == (18*y[x])/((1 + 2*x)^2*(1 + x + x^2)),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_1 \left (x^2+x+1\right )}{(2 x+1)^2}+\frac {c_2 \left (16 x^3+24 x^2-12 \sqrt {3} x^2 \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )+30 x-12 \sqrt {3} x \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )-12 \sqrt {3} \tan ^{-1}\left (\frac {2 x+1}{\sqrt {3}}\right )+11\right )}{(2 x+1)^2}\right \}\right \}\] ✓ Maple : cpu = 0.049 (sec), leaf count = 58
dsolve(diff(diff(y(x),x),x) = 18/(2*x+1)^2/(x^2+x+1)*y(x),y(x))
\[y \left (x \right ) = \frac {-36 c_{2} \left (x^{2}+x +1\right ) \arctan \left (\frac {\left (2 x +1\right ) \sqrt {3}}{3}\right )+16 c_{2} \left (x^{3}+x^{2}+\frac {11}{8} x +\frac {3}{16}\right ) \sqrt {3}+c_{1} \left (x^{2}+x +1\right )}{\left (2 x +1\right )^{2}}\]