\[ \boxed { xy \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -2\,x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.127516 (sec), leaf count = 24 \[ \left \{\left \{y(x)\to \frac {c_2 x^a}{(a-1) c_1 x^a+x}\right \}\right \} \]
Maple: cpu = 1.513 (sec), leaf count = 31 \[ \left \{ y \left ( x \right ) =-{\frac { \left ( a-1 \right ) {x}^{a}}{{ \it \_C2}\,{x}^{a}a-{\it \_C2}\,{x}^{a}-{\it \_C1}\,x}} \right \} \]