\[ y''(x)=\frac {12 y(x)}{(x+1)^2 \left (x^2+2 x+3\right )} \] ✓ Mathematica : cpu = 0.0904419 (sec), leaf count = 71
\[\left \{\left \{y(x)\to \frac {2 c_1 \left (x^2+2 x+3\right )-3 \sqrt {2} c_2 \left (x^2+2 x+3\right ) \tan ^{-1}\left (\frac {x+1}{\sqrt {2}}\right )+2 c_2 \left (x^3+2 x^2+4 x+1\right )}{2 (x+1)^2}\right \}\right \}\]
✓ Maple : cpu = 0.083 (sec), leaf count = 60
\[ \left \{ y \left ( x \right ) ={\frac {1}{ \left ( 1+x \right ) ^{2}} \left ( 3\,{\it \_C2}\, \left ( {x}^{2}+2\,x+3 \right ) \arctan \left ( 1/2\, \left ( 1+x \right ) \sqrt {2} \right ) -{\it \_C2}\, \left ( {x}^{3}+2\,{x}^{2}+4\,x+1 \right ) \sqrt {2}+{\it \_C1}\, \left ( {x}^{2}+2\,x+3 \right ) \right ) } \right \} \]