\[ y'(x)=x \sqrt {a^2 x^2+2 a b x+4 a y(x)+b^2-4 c}-\frac {a x}{2}-\frac {b}{2} \] ✓ Mathematica : cpu = 0.81148 (sec), leaf count = 164
\[\text {Solve}\left [-\frac {\sqrt {a^2 x^2+2 a b x+4 a y(x)+b^2-4 c}}{2 a}-\frac {b \log \left (\sqrt {a^2 x^2+2 a b x+4 a y(x)+b^2-4 c}+a x+b\right )}{2 a}+\frac {b \tanh ^{-1}\left (\frac {2 a^2 x+2 a b}{2 a \sqrt {a^2 x^2+2 a b x+4 a y(x)+b^2-4 c}}\right )}{2 a}+\frac {b \log (4 a y(x)-4 c)}{4 a}+\frac {x^2}{2}=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.375 (sec), leaf count = 41
\[c_{1}+a \,x^{2}+\frac {a}{2}-\sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y \relax (x )-4 c} = 0\]