\[ \left (y'(x)+y(x)^2\right ) \left (a x^2+b x+c\right )^2+A=0 \] ✓ Mathematica : cpu = 1.29124 (sec), leaf count = 704
\[\left \{\left \{y(x)\to -\frac {-\frac {2 a \sqrt {a x^2+b x+c} \exp \left (-\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right ) \left (\frac {(2 a x+b)^2}{4 a c-b^2}+1\right )}+\frac {(2 a x+b) \exp \left (-\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )}{2 \sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}} \sqrt {a x^2+b x+c}}+c_1 \left (\frac {2 a \sqrt {1-\frac {4 A}{b^2-4 a c}} \sqrt {x (a x+b)+c} \exp \left (\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )}{\sqrt {b^2-4 a c} \left (\frac {(2 a x+b)^2}{4 a c-b^2}+1\right )}+\frac {(2 a x+b) \exp \left (\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )}{2 \sqrt {x (a x+b)+c}}\right )}{-\frac {\sqrt {a x^2+b x+c} \exp \left (-\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )}{\sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}}}+c_1 \sqrt {x (a x+b)+c} \left (-\exp \left (\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.422 (sec), leaf count = 493
\[\left \{y \left (x \right ) = \frac {2 \left (c_{1} \left (i \sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, \sqrt {4 a c -b^{2}}\, a -2 \sqrt {-4 a c +b^{2}}\, \left (a x +\frac {b}{2}\right )\right ) \left (\frac {-2 a x -b +i \sqrt {4 a c -b^{2}}}{2 a x +b +i \sqrt {4 a c -b^{2}}}\right )^{-\frac {\sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, a}{2 \sqrt {-4 a c +b^{2}}}}-\left (i \sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, \sqrt {4 a c -b^{2}}\, a +2 \sqrt {-4 a c +b^{2}}\, \left (a x +\frac {b}{2}\right )\right ) \left (\frac {-2 a x -b +i \sqrt {4 a c -b^{2}}}{2 a x +b +i \sqrt {4 a c -b^{2}}}\right )^{\frac {\sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, a}{2 \sqrt {-4 a c +b^{2}}}}\right ) a}{\sqrt {-4 a c +b^{2}}\, \left (2 a x +b +i \sqrt {4 a c -b^{2}}\right ) \left (-2 a x -b +i \sqrt {4 a c -b^{2}}\right ) \left (c_{1} \left (\frac {-2 a x -b +i \sqrt {4 a c -b^{2}}}{2 a x +b +i \sqrt {4 a c -b^{2}}}\right )^{-\frac {\sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, a}{2 \sqrt {-4 a c +b^{2}}}}+\left (\frac {-2 a x -b +i \sqrt {4 a c -b^{2}}}{2 a x +b +i \sqrt {4 a c -b^{2}}}\right )^{\frac {\sqrt {\frac {-4 a c +b^{2}-4 A}{a^{2}}}\, a}{2 \sqrt {-4 a c +b^{2}}}}\right )}\right \}\]