\[ y'(x)=\frac {x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a x}{2}-\frac {a}{2}-\frac {x^2}{2}-\frac {x}{2}}{x+1} \] ✓ Mathematica : cpu = 0.457121 (sec), leaf count = 105
\[\left \{\left \{y(x)\to -\frac {a^2}{4}-\frac {a x}{2}-\frac {2 c_1 x^3}{3}+c_1 x^2+\left (2 c_1-\frac {2 x^3}{3}+x^2-2 x\right ) \log (x+1)-2 c_1 x+c_1^2+\frac {x^6}{9}-\frac {x^5}{3}+\frac {11 x^4}{12}-x^3+\frac {3 x^2}{4}+\log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.405 (sec), leaf count = 43
\[ \left \{ {\it \_C1}+{\frac {2\,{x}^{3}}{3}}-{x}^{2}+2\,x-2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]