\[ x (2 y(x)+x-1) y'(x)-y(x) (y(x)+2 x+1)=0 \] ✓ Mathematica : cpu = 15.3242 (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 = 0.131 (sec), leaf count = 493
\[ \left \{ y \left ( x \right ) ={\frac {3\,\sqrt [3]{5}}{40\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}+{\frac {3\,x{5}^{2/3}}{40}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}}}+x-1,y \left ( x \right ) =-{\frac {3\,\sqrt [3]{5}}{80\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}-{\frac {3\,x{5}^{2/3}}{80}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}}}+x-1-{\frac {i}{2}}\sqrt {3} \left ( {\frac {3\,\sqrt [3]{5}}{40\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}-{\frac {3\,x{5}^{2/3}}{40}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {3\,\sqrt [3]{5}}{80\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}-{\frac {3\,x{5}^{2/3}}{80}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}}}+x-1+{\frac {i}{2}}\sqrt {3} \left ( {\frac {3\,\sqrt [3]{5}}{40\,{\it \_C1}}\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}-{\frac {3\,x{5}^{2/3}}{40}{\frac {1}{\sqrt [3]{x \left ( \sqrt {5}\sqrt {{\frac {80\,{x}^{2}{\it \_C1}-160\,{\it \_C1}\,x+80\,{\it \_C1}-x}{{\it \_C1}}}}+20\,x-20 \right ) {{\it \_C1}}^{2}}}}} \right ) \right \} \]