\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =12\,{\frac {y \left ( x \right ) }{ \left ( 1+x \right ) ^{2} \left ( {x}^{2}+2\,x+3 \right ) }}=0} \]
Mathematica: cpu = 0.077510 (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 = 0.047 (sec), leaf count = 66 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {x}^{2}+2\,x+ 3 \right ) }{ \left ( 1+x \right ) ^{2}}}+{\frac {{\it \_C2}}{ \left ( 1+x \right ) ^{2}} \left ( \left ( 3\,{x}^{2}+6\,x+9 \right ) \arctan \left ( {\frac { \left ( 1+x \right ) \sqrt {2}}{2}} \right ) -\sqrt {2} \left ( {x}^{3}+2\,{x}^{2}+4\,x+1 \right ) \right ) } \right \} \]