\[ (x+1) x^2 y''(x)+2 (3 x+2) x y'(x)=0 \] ✓ Mathematica : cpu = 0.0274268 (sec), leaf count = 44
\[\left \{\left \{y(x)\to c_1 \left (\frac {1}{x^2}-\frac {1}{3 x^3}-\frac {3}{x}-\frac {1}{x+1}-4 \log (x)+4 \log (x+1)\right )+c_2\right \}\right \}\] ✓ Maple : cpu = 0.052 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) ={\it \_C1}+ \left ( -4\,\ln \left ( x \right ) +4\,\ln \left ( 1+x \right ) -{\frac {12\,{x}^{3}+6\,{x}^{2}-2\,x+1}{3\,{x}^{3} \left ( 1+x \right ) }} \right ) {\it \_C2} \right \} \]