\[ -a (x+2) y(x)^2+x (x+1)^2 y(x) y''(x)-x (x+1)^2 y'(x)^2+2 (x+1)^2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.129846 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_2 e^{\frac {-a-c_1}{x}+a \log (x+1)}\right \}\right \}\]
✓ Maple : cpu = 0.1 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 1+x \right ) ^{a}}{{\it \_C2}\,{{\rm e}^{a}}}{{\rm e}^{{\frac {{\it \_C1}}{x}}}} \left ( {{\rm e}^{{\frac {a}{x}}}} \right ) ^{-1}} \right \} \]