\[ -a (x+2) y(x)^2+x (x+1)^2 y(x) y''(x)-x (x+1)^2 y'(x)^2+2 (x+1)^2 y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.185213 (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 = 1.5 (sec), leaf count = 31
\[\left \{y \left (x \right ) = \frac {\left (x +1\right )^{a} {\mathrm e}^{\frac {c_{2}}{x}} {\mathrm e}^{-a} {\mathrm e}^{-\frac {a}{x}}}{c_{1}}\right \}\]