\[ y''(x)=\frac {12 y(x)}{(x+1)^2 \left (x^2+2 x+3\right )} \] ✓ Mathematica : cpu = 0.0514419 (sec), leaf count = 99
DSolve[Derivative[2][y][x] == (12*y[x])/((1 + x)^2*(3 + 2*x + x^2)),y[x],x]
\[\left \{\left \{y(x)\to \frac {c_2 \left (2 x^3+4 x^2-3 \sqrt {2} x^2 \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )+8 x-6 \sqrt {2} x \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )-9 \sqrt {2} \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )+2\right )}{2 (x+1)^2}+c_1 \left (\frac {2}{(x+1)^2}+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.051 (sec), leaf count = 60
dsolve(diff(diff(y(x),x),x) = 12/(1+x)^2/(x^2+2*x+3)*y(x),y(x))
\[y \left (x \right ) = \frac {3 c_{2} \left (x^{2}+2 x +3\right ) \arctan \left (\frac {\left (1+x \right ) \sqrt {2}}{2}\right )-c_{2} \left (x^{3}+2 x^{2}+4 x +1\right ) \sqrt {2}+c_{1} \left (x^{2}+2 x +3\right )}{\left (1+x \right )^{2}}\]