\[ y'(x)=x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}+\sqrt {a^2+2 a x+x^2+4 y(x)}+x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.759691 (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 = 0.385 (sec), leaf count = 37
\[c_{1}+\frac {x^{4}}{2}+\frac {2 x^{3}}{3}+2 x -\sqrt {x^{2}+2 a x +a^{2}+4 y \relax (x )} = 0\]