\[ -a (x+2) y(x)^2-x (x+1)^2 y'(x)^2+2 (x+1)^2 y(x) y'(x)+x (x+1)^2 y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.103474 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_2 e^{a \log (x+1)+\frac {-a-c_1}{x}}\right \}\right \}\] ✓ Maple : cpu = 0.295 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 1+x \right ) ^{a}}{{\it \_C1}\,{{\rm e}^{a}}}{{\rm e}^{{\frac {{\it \_C2}}{x}}}} \left ( {{\rm e}^{{\frac {a}{x}}}} \right ) ^{-1}} \right \} \]