\[ \boxed { \left ( y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +y \left ( x \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ax=0} \]
Mathematica: cpu = 3.996008 (sec), leaf count = 28 \[ \text {DSolve}\left [a x+y(x)^2 y''(x)+y(x) y'(x)^2=0,y(x),x\right ] \]
Maple: cpu = 1.872 (sec), leaf count = 130 \[ \left \{ \ln \left ( x \right ) -\int ^{{\frac {y \left ( x \right ) }{x} }}\!{\frac {1}{2\,\sqrt {3}{{\it \_g}}^{3}+2\,\sqrt {3}a} \left ( 3\,{{ \it \_g}}^{2}\sqrt [3]{{\frac {a}{{{\it \_g}}^{3}}}}\tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}\,\sqrt {3}+\ln \left ( {\frac { \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1}{3+2\,\sqrt {3}\tan \left ( {\it \_Z} \right ) + \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}} \right ) +6\,{\it \_C1}+6\,\int \!{\frac {{{\it \_g}}^{ 2}}{{{\it \_g}}^{3}+a} \left ( {\frac {a}{{{\it \_g}}^{3}}} \right ) ^{2 /3}}\,{\rm d}{\it \_g} \right ) \right ) +{{\it \_g}}^{2}\sqrt [3]{{ \frac {a}{{{\it \_g}}^{3}}}}\sqrt {3}-2\,{{\it \_g}}^{2}\sqrt {3} \right ) }{d{\it \_g}}-{\it \_C2}=0 \right \} \]