\[ y'(x)=\frac {x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a x}{2}-\frac {a}{2}-\frac {x^2}{2}-\frac {x}{2}}{x+1} \] ✓ Mathematica : cpu = 0.775273 (sec), leaf count = 116
\[\text {Solve}\left [-\frac {1}{2} \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {1}{2} a \log \left (\sqrt {a^2+2 a x+x^2+4 y(x)}+a+x\right )+\frac {1}{2} a \tanh ^{-1}\left (\frac {a+x}{\sqrt {a^2+2 a x+x^2+4 y(x)}}\right )+\frac {1}{4} a \log (y(x))+\frac {x^3}{3}-\frac {x^2}{2}+x-\log (x+1)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.589 (sec), leaf count = 43
\[c_{1}+\frac {2 x^{3}}{3}-x^{2}+2 x -2 \ln \left (1+x \right )-\sqrt {x^{2}+2 a x +a^{2}+4 y \relax (x )} = 0\]