\[ \boxed { \left ( 3\,x+2 \right ) \left ( y \left ( x \right ) -2\,x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) -7\,{x}^{2}-9\,x-3=0} \]
Mathematica: cpu = 7.981514 (sec), leaf count = 693 \[ \left \{\left \{y(x)\to \frac {\sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}{6 \sqrt [3]{2}}-\frac {-81 x^2-108 x-36}{3\ 2^{2/3} \sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}+\frac {x}{2}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-81 x^2-108 x-36\right )}{6\ 2^{2/3} \sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}+\frac {x}{2}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-81 x^2-108 x-36\right )}{6\ 2^{2/3} \sqrt [3]{\sqrt {\left (-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432\right ){}^2+4 \left (-81 x^2-108 x-36\right )^3}-324 e^{2 c_1} x-216 e^{2 c_1}+1458 x^3+2916 x^2+1944 x+432}}+\frac {x}{2}\right \}\right \} \]
Maple: cpu = 0.156 (sec), leaf count = 517 \[ \left \{ y \left ( x \right ) =-{\frac {1}{3}}+{\frac {3\,x+2}{6} \left ( 7\, \left ( -1/4\,\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1 }-27\, \left ( 3\,x+2 \right ) ^{3}{{\it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^{4}+ \left ( 3\,x+2 \right ) ^{2 }{{\it \_C1}}^{2}}}-9/4\,{\frac { \left ( 3\,x+2 \right ) ^{2}{{\it \_C1 }}^{2}}{\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\, x+2 \right ) ^{3}{{\it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^{4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^ {2}}}}}-3/2\, \left ( 3\,x+2 \right ) {\it \_C1}+i/2\sqrt {3} \left ( 1/2 \,\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{\it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{ 4}{{\it \_C1}}^{4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}}-9/2\, {\frac { \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}{\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{ \it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^ {4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}}}} \right ) \right ) ^ {2}-1 \right ) \left ( -{\frac {1}{4}\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{\it \_C1}}^{3}+2 \,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^{4}+ \left ( 3\,x +2 \right ) ^{2}{{\it \_C1}}^{2}}}}-{\frac {9\, \left ( 3\,x+2 \right ) ^ {2}{{\it \_C1}}^{2}}{4}{\frac {1}{\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{\it \_C1}}^{3}+2\,\sqrt {- 27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^{4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}}}}}-{\frac { \left ( 9\,x+6 \right ) { \it \_C1}}{2}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2}\sqrt [3]{2 \, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{ \it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^ {4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}}}-{\frac {9\, \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}{2}{\frac {1}{\sqrt [3]{2\, \left ( 3\,x+2 \right ) {\it \_C1}-27\, \left ( 3\,x+2 \right ) ^{3}{{ \it \_C1}}^{3}+2\,\sqrt {-27\, \left ( 3\,x+2 \right ) ^{4}{{\it \_C1}}^ {4}+ \left ( 3\,x+2 \right ) ^{2}{{\it \_C1}}^{2}}}}}} \right ) \right ) ^{-2}} \right \} \]