\[ \left (y'(x)+y(x)^2\right ) \left (a x^2+b x+c\right )^2+A=0 \] ✓ Mathematica : cpu = 1.44383 (sec), leaf count = 612
\[\left \{\left \{y(x)\to \frac {b^2 c_1 \left (-\exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )\right )+b c_1 \sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}} \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+4 A c_1 \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+4 a c c_1 \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+2 a c_1 x \sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}} \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+\sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}}+2 a x+b}{2 (x (a x+b)+c) \left (c_1 \sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}} \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+1\right )}\right \}\right \}\]
✓ Maple : cpu = 0.385 (sec), leaf count = 493
\[ \left \{ y \left ( x \right ) =2\,{\frac {a}{\sqrt {-4\,ac+{b}^{2}} \left ( 2\,ax+b+i\sqrt {4\,ac-{b}^{2}} \right ) \left ( i\sqrt {4\,ac-{b}^{2}}-2\,ax-b \right ) } \left ( \left ( i\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}a\sqrt {4\,ac-{b}^{2}}-2\, \left ( ax+b/2 \right ) \sqrt {-4\,ac+{b}^{2}} \right ) {\it \_C1}\, \left ( {\frac {i\sqrt {4\,ac-{b}^{2}}-2\,ax-b}{2\,ax+b+i\sqrt {4\,ac-{b}^{2}}}} \right ) ^{-1/2\,{\frac {a}{\sqrt {-4\,ac+{b}^{2}}}\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}}}- \left ( {\frac {i\sqrt {4\,ac-{b}^{2}}-2\,ax-b}{2\,ax+b+i\sqrt {4\,ac-{b}^{2}}}} \right ) ^{1/2\,{\frac {a}{\sqrt {-4\,ac+{b}^{2}}}\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}}} \left ( i\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}a\sqrt {4\,ac-{b}^{2}}+2\, \left ( ax+b/2 \right ) \sqrt {-4\,ac+{b}^{2}} \right ) \right ) \left ( {\it \_C1}\, \left ( {\frac {i\sqrt {4\,ac-{b}^{2}}-2\,ax-b}{2\,ax+b+i\sqrt {4\,ac-{b}^{2}}}} \right ) ^{-1/2\,{\frac {a}{\sqrt {-4\,ac+{b}^{2}}}\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}}}+ \left ( {\frac {i\sqrt {4\,ac-{b}^{2}}-2\,ax-b}{2\,ax+b+i\sqrt {4\,ac-{b}^{2}}}} \right ) ^{1/2\,{\frac {a}{\sqrt {-4\,ac+{b}^{2}}}\sqrt {{\frac {-4\,ac+{b}^{2}-4\,A}{{a}^{2}}}}}} \right ) ^{-1}} \right \} \]