\[ a y(x) y'(x)+2 x y'(x)^2+x y(x) y''(x)=0 \] ✓ Mathematica : cpu = 0.211698 (sec), leaf count = 40
\[\left \{\left \{y(x)\to c_2 \left (3 x^{1-a}-(a-1) c_1\right ){}^{-\frac {a-1}{3 (1-a)}}\right \}\right \}\] ✓ Maple : cpu = 0.354 (sec), leaf count = 148
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt [3]{3}}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) ={\frac {\sqrt [3]{3} \left ( -1+i\sqrt {3} \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }},y \left ( x \right ) =-{\frac {\sqrt [3]{3} \left ( 1+i\sqrt {3} \right ) }{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2} \left ( {\it \_C2}\, \left ( a-1 \right ) {x}^{a}-{\it \_C1}\,x \right ) }} \right \} \]