\[ a y(x)+x y'(x)^2-y(x) y'(x)=0 \] ✓ Mathematica : cpu = 0.440878 (sec), leaf count = 165
\[\left \{\text {Solve}\left [-\frac {\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}-4 a \log \left (\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}\right )+\frac {y(x)}{x}}{4 a}=c_1+\frac {\log (x)}{2},y(x)\right ],\text {Solve}\left [\frac {y(x)}{4 a x}-\frac {\sqrt {\frac {y(x)}{x}} \sqrt {\frac {y(x)}{x}-4 a}}{4 a}+\log \left (\sqrt {\frac {y(x)}{x}-4 a}+\sqrt {\frac {y(x)}{x}}\right )=c_1-\frac {\log (x)}{2},y(x)\right ]\right \}\]
✓ Maple : cpu = 0.044 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) =-{{a}^{2}x \left ( -{\it lambertW} \left ( -{\frac {x{\rm e}}{{\it \_C1}\,a}} \right ) +1 \right ) ^{2} \left ( - \left ( -{\it lambertW} \left ( -{\frac {x{\rm e}}{{\it \_C1}\,a}} \right ) +1 \right ) a+a \right ) ^{-1}} \right \} \]