\[ \boxed { 2\,x \left ( x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( x-1 \right ) \left ( y \left ( x \right ) \right ) ^{2}-x=0} \]
Mathematica: cpu = 0.082511 (sec), leaf count = 71 \[ \left \{\left \{y(x)\to \frac {2 x \left (\frac {c_1 (E(x)-K(x))}{\pi x}-G_{2,2}^{2,0}\left (x\left | \begin {array}{c} -\frac {1}{2},\frac {1}{2} \\ -1,0 \\ \end {array} \right .\right )\right )}{G_{2,2}^{2,0}\left (x\left | \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right .\right )+\frac {2 c_1 E(x)}{\pi }}\right \}\right \} \]
Maple: cpu = 0.109 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) ={\frac {x}{2\,x-2} \left ( {\it LegendreQ} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) {\it \_C1}-{\it LegendreQ} \left ( {\frac {1}{2}},1,{\frac {2-x}{x}} \right ) {\it \_C1} +{\it LegendreP} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) -{ \it LegendreP} \left ( {\frac {1}{2}},1,{\frac {2-x}{x}} \right ) \right ) \left ( {\it LegendreQ} \left ( -{\frac {1}{2}},1,{\frac {2-x }{x}} \right ) {\it \_C1}+{\it LegendreP} \left ( -{\frac {1}{2}},1,{ \frac {2-x}{x}} \right ) \right ) ^{-1}} \right \} \]