\[ y''(x)=\frac {12 y(x)}{(x+1)^2 \left (x^2+2 x+3\right )} \] ✓ Mathematica : cpu = 0.0916742 (sec), leaf count = 99
\[\left \{\left \{y(x)\to \frac {c_2 \left (2 x^3+4 x^2-3 \sqrt {2} x^2 \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )+8 x-6 \sqrt {2} x \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )-9 \sqrt {2} \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )+2\right )}{2 (x+1)^2}+c_1 \left (\frac {2}{(x+1)^2}+1\right )\right \}\right \}\]
✓ Maple : cpu = 0.068 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{2}+2\,x+3 \right ) }{ \left ( 1+x \right ) ^{2}}}+{\frac {{\it \_C2}}{ \left ( 1+x \right ) ^{2}} \left ( \left ( -3\,{x}^{2}-6\,x-9 \right ) \arctan \left ( {\frac { \left ( 1+x \right ) \sqrt {2}}{2}} \right ) +\sqrt {2} \left ( {x}^{3}+2\,{x}^{2}+4\,x+1 \right ) \right ) } \right \} \]