\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) +x=0} \]
Mathematica: cpu = 0.532068 (sec), leaf count = 166 \[ \left \{\text {Solve}\left [\frac {\left (\sqrt {\frac {2 y(x)}{x}-1}-1\right ) \left (\left (\sqrt {\frac {2 y(x)}{x}-1}-1\right ) \log \left (\sqrt {\frac {2 y(x)}{x}-1}-1\right )-1\right )}{\sqrt {\frac {2 y(x)}{x}-1}-\frac {y(x)}{x}}=c_1+\log (x),y(x)\right ],\text {Solve}\left [\frac {\left (\sqrt {\frac {2 y(x)}{x}-1}+1\right ) \left (\left (\sqrt {\frac {2 y(x)}{x}-1}+1\right ) \log \left (\sqrt {\frac {2 y(x)}{x}-1}+1\right )+1\right )}{\frac {y(x)}{x}+\sqrt {\frac {2 y(x)}{x}-1}}=c_1-\log (x),y(x)\right ]\right \} \]
Maple: cpu = 0.514 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) = \left ( {\frac {1}{2} \left ( {\it lambertW} \left ( {\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) +1 \right ) ^{2} \left ( {\it lambertW} \left ( {\frac {1}{{\it \_C1}} \sqrt {{\it \_C1}\,x}} \right ) \right ) ^{-2}}+{\frac {1}{2}} \right ) x,y \left ( x \right ) = \left ( {\frac {1}{2} \left ( {\it lambertW} \left ( -{\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\,x}} \right ) +1 \right ) ^{2} \left ( {\it lambertW} \left ( -{\frac {1}{{\it \_C1}} \sqrt {{\it \_C1}\,x}} \right ) \right ) ^{-2}}+{\frac {1}{2}} \right ) x \right \} \]