\[ a \left (x y'(x)-y(x)\right )^2+x^2 (x-y(x)) y''(x)=0 \] ✓ Mathematica : cpu = 0.904813 (sec), leaf count = 37
\[\left \{\left \{y(x)\to x \left (\left ((a-1) \left (\frac {(-1)^{a+1} c_1}{x}-c_2\right )\right ){}^{\frac {1}{1-a}}+1\right )\right \}\right \}\]
✓ Maple : cpu = 0.413 (sec), leaf count = 47
\[ \left \{ {\it \_C1}+ \left ( ax-x \right ) {\it \_C2}-{x}^{a}y \left ( x \right ) \left ( x-y \left ( x \right ) \right ) ^{-a}+{x}^{a+1} \left ( x-y \left ( x \right ) \right ) ^{-a}=0 \right \} \]