\[ x (2 y(x)-x-1) y'(x)+(-y(x)+2 x-1) y(x)=0 \] ✓ Mathematica : cpu = 8.99478 (sec), leaf count = 484
DSolve[(-1 + 2*x - y[x])*y[x] + x*(-1 - x + 2*y[x])*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{2} x}{\sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}-\frac {\sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{3 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{27 c_1{}^2 x^2+\sqrt {\left (27 c_1{}^2 x^2+27 c_1{}^2 x\right ){}^2-108 c_1{}^3 x^3}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \}\right \}\] ✓ Maple : cpu = 0.1 (sec), leaf count = 391
dsolve(x*(2*y(x)-x-1)*diff(y(x),x)+y(x)*(2*x-y(x)-1) = 0,y(x))
\[y \left (x \right ) = \frac {3 \,5^{\frac {1}{3}} \left (x \left (\sqrt {5}\, \sqrt {\frac {80 x^{2} c_{1}+160 c_{1} x -x +80 c_{1}}{c_{1}}}-20 x -20\right ) c_{1}^{2}\right )^{\frac {1}{3}}}{40 c_{1}}+\frac {3 x 5^{\frac {2}{3}}}{40 \left (x \left (\sqrt {5}\, \sqrt {\frac {80 x^{2} c_{1}+160 c_{1} x -x +80 c_{1}}{c_{1}}}-20 x -20\right ) c_{1}^{2}\right )^{\frac {1}{3}}}-1-x\]