\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.254972 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_2 \left (3 x^{1-a}-(a-1) c_1\right ){}^{-\frac {a-1}{3 (1-a)}}\right \}\right \}\] ✓ Maple : cpu = 1.236 (sec), leaf count = 148
\[\left \{y \left (x \right ) = \frac {3^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (-c_{1} x +c_{2} \left (a -1\right ) x^{a}\right ) x^{2 a}\right )^{\frac {1}{3}} x^{-a}}{a -1}, y \left (x \right ) = -\frac {3^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (-c_{1} x +c_{2} \left (a -1\right ) x^{a}\right ) x^{2 a}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right ) x^{-a}}{2 \left (a -1\right )}, y \left (x \right ) = \frac {3^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (-c_{1} x +c_{2} \left (a -1\right ) x^{a}\right ) x^{2 a}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right ) x^{-a}}{2 a -2}\right \}\]