\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/2\,ax-b/2+{x}^{2}\sqrt {{a}^{2}{x}^{2}+2\,abx+{b}^{2}+4\,ay \left ( x \right ) -4\,c}=0} \]
Mathematica: cpu = 0.420553 (sec), leaf count = 61 \[ \left \{\left \{y(x)\to \frac {-24 a^2 c_1 x^3+36 a^2 c_1^2+4 a^2 x^6-9 a^2 x^2-18 a b x-9 b^2+36 c}{36 a}\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 39 \[ \left \{ {\it \_C1}+{\frac {2\,a{x}^{3}}{3}}-\sqrt {{a}^{2}{x}^{2}+2\, abx+{b}^{2}+4\,ay \left ( x \right ) -4\,c}=0 \right \} \]