\[ a \left (x y'(x)-y(x)\right )^2+x^2 (x-y(x)) y''(x)=0 \] ✓ Mathematica : cpu = 0.611169 (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 = 1.042 (sec), leaf count = 42
\[y \relax (x ) = -\RootOf \left (-c_{2} a x \,\textit {\_Z}^{a}+c_{1} a \,\textit {\_Z}^{a}+c_{2} x \,\textit {\_Z}^{a}-c_{1} \textit {\_Z}^{a}-\textit {\_Z} \,x^{a}\right )+x\]