\[ a \left (x y'(x)-y(x)\right )^2+x^2 (x-y(x)) y''(x)=0 \] ✓ Mathematica : cpu = 0.542325 (sec), leaf count = 37
\[\left \{\left \{y(x)\to x \left (1+\left ((a-1) \left (\frac {(-1)^{a+1} c_1}{x}-c_2\right )\right ){}^{\frac {1}{1-a}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.546 (sec), leaf count = 35
\[ \left \{ \left ( -{x}^{a}y \left ( x \right ) +{x}^{a+1} \right ) \left ( x-y \left ( x \right ) \right ) ^{-a}+x \left ( a-1 \right ) {\it \_C2}+{\it \_C1}=0 \right \} \]