\[ y''(x)=\frac {12 y(x)}{(x+1)^2 \left (x^2+2 x+3\right )} \] ✓ Mathematica : cpu = 0.059282 (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 = 0.075 (sec), leaf count = 59
\[ \left \{ y \left ( x \right ) ={\frac {1}{ \left ( 1+x \right ) ^{2}} \left ( -3\,{\it \_C2}\, \left ( {x}^{2}+2\,x+3 \right ) \arctan \left ( 1/2\, \left ( 1+x \right ) \sqrt {2} \right ) +{\it \_C2}\, \left ( {x}^{3}+2\,{x}^{2}+4\,x+1 \right ) \sqrt {2}+{\it \_C1}\, \left ( {x}^{2}+2\,x+3 \right ) \right ) } \right \} \]