#### 2.247   ODE No. 247

$-7 x^2+(3 x+2) (y(x)-2 x-1) y'(x)+x y(x)-y(x)^2-9 x-3=0$ Mathematica : cpu = 11.4063 (sec), leaf count = 693

$\left \{\left \{y(x)\to \frac {\sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}{6 \sqrt [3]{2}}-\frac {-81 x^2-108 x-36}{3\ 2^{2/3} \sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}+\frac {x}{2}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}{12 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-81 x^2-108 x-36\right )}{6\ 2^{2/3} \sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}+\frac {x}{2}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}{12 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-81 x^2-108 x-36\right )}{6\ 2^{2/3} \sqrt [3]{1458 x^3+2916 x^2+\sqrt {4 \left (-81 x^2-108 x-36\right )^3+\left (1458 x^3+2916 x^2+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}\right ){}^2}+1944 x-324 e^{2 c_1} x+432-216 e^{2 c_1}}}+\frac {x}{2}\right \}\right \}$ Maple : cpu = 0.181 (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 \}$