\[ x (2 y(x)+x-1) y'(x)-y(x) (y(x)+2 x+1)=0 \] ✓ Mathematica : cpu = 14.9924 (sec), leaf count = 487
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{2} x}{\sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}+\frac {\sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}{3 \sqrt [3]{2} c_1}+\frac {c_1 x-c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}+\frac {c_1 x-c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-27 c_1{}^2 x^2+\sqrt {108 c_1{}^3 x^3+\left (27 c_1{}^2 x-27 c_1{}^2 x^2\right ){}^2}+27 c_1{}^2 x}}{6 \sqrt [3]{2} c_1}+\frac {c_1 x-c_1}{c_1}\right \}\right \}\] ✓ Maple : cpu = 0.132 (sec), leaf count = 391
\[\left \{y \left (x \right ) = \frac {-3 c_{1} \left (\left (1+i \sqrt {3}\right ) 5^{\frac {2}{3}} x -\frac {80 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}} \left (x -1\right )}{3}\right )+3 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {2}{3}} \left (i \sqrt {3}-1\right ) 5^{\frac {1}{3}}}{80 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}} c_{1}}, y \left (x \right ) = \frac {3 c_{1} \left (\left (i \sqrt {3}-1\right ) 5^{\frac {2}{3}} x +\frac {80 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}} \left (x -1\right )}{3}\right )-3 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {2}{3}} \left (1+i \sqrt {3}\right ) 5^{\frac {1}{3}}}{80 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} \left (x -1\right )^{2}-x}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}} c_{1}}, y \left (x \right ) = \frac {3 \,5^{\frac {2}{3}} x}{40 \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} x^{2}-160 c_{1} x -x +80 c_{1}}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}}}+x +\frac {3 \,5^{\frac {1}{3}} \left (\left (20 x +\sqrt {5}\, \sqrt {\frac {80 c_{1} x^{2}-160 c_{1} x -x +80 c_{1}}{c_{1}}}-20\right ) c_{1}^{2} x \right )^{\frac {1}{3}}}{40 c_{1}}-1\right \}\]