\[ y''(x)=-\frac {A y(x)}{\left (a x^2+b x+c\right )^2} \] ✓ Mathematica : cpu = 1.43711 (sec), leaf count = 199
\[\left \{\left \{y(x)\to \sqrt {x (a x+b)+c} \exp \left (-\frac {\sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right ) \left (c_1 \exp \left (\frac {2 \sqrt {4 a c-b^2} \sqrt {1-\frac {4 A}{b^2-4 a c}} \tan ^{-1}\left (\frac {2 a x+b}{\sqrt {4 a c-b^2}}\right )}{\sqrt {b^2-4 a c}}\right )+\frac {c_2}{\sqrt {b^2-4 a c} \sqrt {1-\frac {4 A}{b^2-4 a c}}}\right )\right \}\right \}\]
✓ Maple : cpu = 0.161 (sec), leaf count = 178
\[ \left \{ y \left ( x \right ) =\sqrt {a{x}^{2}+bx+c} \left ( \left ( {1 \left ( i\sqrt {4\,ca-{b}^{2}}-2\,ax-b \right ) \left ( 2\,ax+b+i\sqrt {4\,ca-{b}^{2}} \right ) ^{-1}} \right ) ^{-{\frac {a}{2}\sqrt {{\frac {-4\,ca+{b}^{2}-4\,A}{{a}^{2}}}}{\frac {1}{\sqrt {-4\,ca+{b}^{2}}}}}}{\it \_C2}+ \left ( {1 \left ( i\sqrt {4\,ca-{b}^{2}}-2\,ax-b \right ) \left ( 2\,ax+b+i\sqrt {4\,ca-{b}^{2}} \right ) ^{-1}} \right ) ^{{\frac {a}{2}\sqrt {{\frac {-4\,ca+{b}^{2}-4\,A}{{a}^{2}}}}{\frac {1}{\sqrt {-4\,ca+{b}^{2}}}}}}{\it \_C1} \right ) \right \} \]