\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.142668 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_2 x^{-a/3} \sqrt [3]{3 x-(a-1) c_1 x^a}\right \}\right \}\]
✓ Maple : cpu = 0.053 (sec), leaf count = 148
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt [3]{3}}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( {x}^{a} \right ) ^{2} \left ( a-1 \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) ={\frac {\sqrt [3]{3} \left ( i\sqrt {3}-1 \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( {x}^{a} \right ) ^{2} \left ( a-1 \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) =-{\frac {\sqrt [3]{3} \left ( i\sqrt {3}+1 \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( {x}^{a} \right ) ^{2} \left ( a-1 \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }} \right \} \]