\[ y'(x)=x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}+\sqrt {a^2+2 a x+x^2+4 y(x)}+x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.565376 (sec), leaf count = 85
\[\left \{\left \{y(x)\to -\frac {a^2}{4}-\frac {a x}{2}-\frac {1}{6} \left (3 c_1-4\right ) x^4-\frac {2 c_1 x^3}{3}-2 c_1 x+c_1^2+\frac {x^8}{16}+\frac {x^7}{6}+\frac {x^6}{9}+\frac {x^5}{2}+\frac {3 x^2}{4}\right \}\right \}\]
✓ Maple : cpu = 0.362 (sec), leaf count = 37
\[ \left \{ {\it \_C1}+{\frac {{x}^{4}}{2}}+{\frac {2\,{x}^{3}}{3}}+2\,x-\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]