\[ \boxed { {x}^{2} \left ( 1+x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x \left ( 3\,x+2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.028504 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to c_1 \left (-\frac {1}{3 x^3}+\frac {1}{x^2}-\frac {3}{x}-\frac {1}{x+1}-4 \log (x)+4 \log (x+1)\right )+c_2\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 44 \[ \left \{ y \left ( x \right ) ={\it \_C1}+ \left ( -4\,\ln \left ( x \right ) +4\,\ln \left ( 1+x \right ) -{\frac {12\,{x}^{3}+6\,{x}^{2}-2 \,x+1}{ \left ( 3+3\,x \right ) {x}^{3}}} \right ) {\it \_C2} \right \} \]