\[ -a (x+2) y(x)^2+x (x+1)^2 y(x) y''(x)-x (x+1)^2 y'(x)^2+2 (x+1)^2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.165047 (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 = 1.096 (sec), leaf count = 31
\[y \relax (x ) = \frac {\left (1+x \right )^{a} {\mathrm e}^{-a} {\mathrm e}^{\frac {c_{2}}{x}} {\mathrm e}^{-\frac {a}{x}}}{c_{1}}\]