\[ y'(x)=x^2 \sqrt {a^2 x^2+2 a b x+4 a y(x)+b^2-4 c}-\frac {a x}{2}-\frac {b}{2} \] ✓ Mathematica : cpu = 0.355408 (sec), leaf count = 93
DSolve[Derivative[1][y][x] == -1/2*b - (a*x)/2 + x^2*Sqrt[b^2 - 4*c + 2*a*b*x + a^2*x^2 + 4*a*y[x]],y[x],x]
\[\left \{\left \{y(x)\to \frac {b^2 \log ^2\left (\sinh \left (\frac {2 a x^3}{3 b}-\frac {2 a c_1}{b}\right )-\cosh \left (\frac {2 a x^3}{3 b}-\frac {2 a c_1}{b}\right )\right )}{4 a}-\frac {b^2}{4 a}+\frac {c}{a}-\frac {a x^2}{4}-\frac {b x}{2}\right \}\right \}\] ✓ Maple : cpu = 0.296 (sec), leaf count = 39
dsolve(diff(y(x),x) = -1/2*a*x-1/2*b+x^2*(a^2*x^2+2*a*b*x+b^2+4*a*y(x)-4*c)^(1/2),y(x))
\[c_{1}+\frac {2 a \,x^{3}}{3}-\sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y \left (x \right )-4 c} = 0\]