\[ \boxed { xy \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +2\,x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ay \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.139018 (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 = 1.560 (sec), leaf count = 234 \[ \left \{ y \left ( x \right ) ={\frac {1}{ \left ( a-1 \right ) {x}^{a}} \sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{ \it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^ {2}}},y \left ( x \right ) =-{\frac {1}{ \left ( -2+2\,a \right ) {x}^{a}} \sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{ \it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^ {2}}}-{\frac {{\frac {i}{2}}\sqrt {3}}{ \left ( a-1 \right ) {x}^{a}} \sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{ \it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^ {2}}},y \left ( x \right ) =-{\frac {1}{ \left ( -2+2\,a \right ) {x}^{a}} \sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{ \it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^ {2}}}+{\frac {{\frac {i}{2}}\sqrt {3}}{ \left ( a-1 \right ) {x}^{a}} \sqrt [3]{ \left ( 3\,{\it \_C2}\,{x}^{a}a-3\,{\it \_C2}\,{x}^{a}-3\,{ \it \_C1}\,x \right ) \left ( a-1 \right ) ^{2} \left ( {x}^{a} \right ) ^ {2}}} \right \} \]