\[ a y(x) y'(x)+x y(x) y''(x)-2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.156152 (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 = 0.044 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) =-{\frac { \left ( a-1 \right ) {x}^{a}}{{\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x}} \right \} \]