\[ a \left (x y'(x)-y(x)\right )^2+x^2 (x-y(x)) y''(x)=0 \] ✓ Mathematica : cpu = 1.02427 (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 = 0.164 (sec), leaf count = 37
\[ \left \{ \left ( {x}^{a}y \left ( x \right ) -{x}^{a+1} \right ) \left ( x-y \left ( x \right ) \right ) ^{-a}-x \left ( a-1 \right ) {\it \_C1}+{\it \_C2}=0 \right \} \]