\[ y'(x)=x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}+x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}+\sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.649474 (sec), leaf count = 117
\[\text {Solve}\left [-\frac {1}{2} \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {1}{2} a \log \left (\sqrt {a^2+2 a x+x^2+4 y(x)}+a+x\right )+\frac {1}{2} a \tanh ^{-1}\left (\frac {2 a+2 x}{2 \sqrt {a^2+2 a x+x^2+4 y(x)}}\right )+\frac {1}{4} a \log (y(x))+\frac {x^4}{4}+\frac {x^3}{3}+x=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.522 (sec), leaf count = 37
\[ \left \{ {\it \_C1}+{\frac {{x}^{4}}{2}}+{\frac {2\,{x}^{3}}{3}}+2\,x-\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]