\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.1456 (sec), leaf count = 35
\[\left \{\left \{y(x)\to c_2 \exp \left (\frac {1}{3} \left (\log \left (3 x-(a-1) c_1 x^a\right )-a \log (x)\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.069 (sec), leaf count = 148
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt [3]{3}}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) ={\frac {\sqrt [3]{3} \left ( i\sqrt {3}-1 \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) =-{\frac {\sqrt [3]{3} \left ( i\sqrt {3}+1 \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }} \right \} \]