\[ 2 (x-1) x y'(x)+(x-1) y(x)^2-x=0 \] ✓ Mathematica : cpu = 0.108592 (sec), leaf count = 71
DSolve[-x + (-1 + x)*y[x]^2 + 2*(-1 + x)*x*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {2 x \left (-G_{2,2}^{2,0}\left (x\left |\begin {array}{c} -\frac {1}{2},\frac {1}{2} \\ -1,0 \\\end {array}\right .\right )+\frac {c_1 (\operatorname {EllipticE}(x)-\operatorname {EllipticK}(x))}{\pi x}\right )}{G_{2,2}^{2,0}\left (x\left |\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right .\right )+\frac {2 c_1 \operatorname {EllipticE}(x)}{\pi }}\right \}\right \}\] ✓ Maple : cpu = 0.104 (sec), leaf count = 97
dsolve(2*x*(x-1)*diff(y(x),x)+(x-1)*y(x)^2-x = 0,y(x))
\[y \left (x \right ) = \frac {x \left (\operatorname {LegendreQ}\left (-\frac {1}{2}, 1, \frac {2-x}{x}\right ) c_{1}-\operatorname {LegendreQ}\left (\frac {1}{2}, 1, \frac {2-x}{x}\right ) c_{1}+\operatorname {LegendreP}\left (-\frac {1}{2}, 1, \frac {2-x}{x}\right )-\operatorname {LegendreP}\left (\frac {1}{2}, 1, \frac {2-x}{x}\right )\right )}{2 \left (\operatorname {LegendreQ}\left (-\frac {1}{2}, 1, \frac {2-x}{x}\right ) c_{1}+\operatorname {LegendreP}\left (-\frac {1}{2}, 1, \frac {2-x}{x}\right )\right ) \left (x -1\right )}\]