\[ a y(x)+x y'(x)^2-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.902108 (sec), leaf count = 158
\[\left \{\text {Solve}\left [\frac {y(x)}{a x}+\frac {\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}}{a}+4 c_1+2 \log (x)=4 \log \left (\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}\right ),y(x)\right ],\text {Solve}\left [\frac {\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}}{a}+4 c_1=\frac {y(x)}{a x}+4 \log \left (\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}\right )+2 \log (x),y(x)\right ]\right \}\]
✓ Maple : cpu = 0.097 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) =-{ax \left ( {\it lambertW} \left ( -{\frac {x{\rm e}}{a{\it \_C1}}} \right ) -1 \right ) ^{2} \left ( {\it lambertW} \left ( -{\frac {x{\rm e}}{a{\it \_C1}}} \right ) \right ) ^{-1}} \right \} \]