\[ y'(x)=x \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.247795 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-a^2-2 a x-\left (4 c_1+1\right ) x^2+4 c_1^2+x^4\right )\right \}\right \}\]
✓ Maple : cpu = 0.234 (sec), leaf count = 28
\[ \left \{ {\it \_C1}+{x}^{2}+{\frac {1}{2}}-\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]