\[ a y(x) y'(x)+x y(x) y''(x)+2 x y'(x)^2=0 \] ✓ Mathematica : cpu = 0.139138 (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 = 0.328 (sec), leaf count = 234
\[ \left \{ y \left ( x \right ) ={\frac {1}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{\it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2}}},y \left ( x \right ) =-{\frac {1}{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{\it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2}}}-{\frac {{\frac {i}{2}}\sqrt {3}}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{\it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2}}},y \left ( x \right ) =-{\frac {1}{ \left ( 2\,a-2 \right ) {x}^{a}}\sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{\it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2}}}+{\frac {{\frac {i}{2}}\sqrt {3}}{ \left ( a-1 \right ) {x}^{a}}\sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{\it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^{2}}} \right \} \]