\[ y'(x)=\frac {x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a x}{2}-\frac {a}{2}-\frac {x^2}{2}-\frac {x}{2}}{x+1} \] ✓ Mathematica : cpu = 0.464142 (sec), leaf count = 110
\[\left \{\left \{y(x)\to \frac {1}{36} \left (-9 a^2-18 a x-24 c_1 x^3+36 c_1 x^2-72 c_1 x+72 c_1 \log (x+1)+36 c_1^2+4 x^6-12 x^5+33 x^4-36 x^3-24 x^3 \log (x+1)+27 x^2+36 x^2 \log (x+1)+36 \log ^2(x+1)-72 x \log (x+1)\right )\right \}\right \}\] ✓ Maple : cpu = 0.399 (sec), leaf count = 43
\[ \left \{ {\it \_C1}+{\frac {2\,{x}^{3}}{3}}-{x}^{2}+2\,x-2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]