\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.446057 (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 = 0.515 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) =0,y \left ( x \right ) =-{{a}^{2}x \left ( - {\it lambertW} \left ( -{\frac {x{\rm e}}{{\it \_C1}\,a}} \right ) +1 \right ) ^{2} \left ( - \left ( -{\it lambertW} \left ( -{\frac {x{\rm e} }{{\it \_C1}\,a}} \right ) +1 \right ) a+a \right ) ^{-1}} \right \} \]