\[ y'(x)=x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}+\sqrt {a^2+2 a x+x^2+4 y(x)}+x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.506387 (sec), leaf count = 74
\[\left \{\left \{y(x)\to \frac {1}{144} \left (-36 a^2-72 a x-72 c_1 x^4-96 c_1 x^3-288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+96 x^4+108 x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.375 (sec), leaf count = 37
\[ \left \{ {\it \_C1}+{\frac {{x}^{4}}{2}}+{\frac {2\,{x}^{3}}{3}}+2\,x-\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]