\[ \boxed { x \left ( 2\,y \left ( x \right ) -x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \left ( 2\,x-y \left ( x \right ) -1 \right ) =0} \]
Mathematica: cpu = 7.972512 (sec), leaf count = 484 \[ \left \{\left \{y(x)\to -\frac {\sqrt [3]{2} x}{\sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}-\frac {\sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}{3 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) x}{2^{2/3} \sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{27 c_1^2 x^2+\sqrt {\left (27 c_1^2 x^2+27 c_1^2 x\right ){}^2-108 c_1^3 x^3}+27 c_1^2 x}}{6 \sqrt [3]{2} c_1}-\frac {c_1 x+c_1}{c_1}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 499 \[ \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}}}}}-1-x,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}}}}}-1-x-{\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}}}}}-1-x+{\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 \} \]