\[ y'(x)=\frac {\sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a x}{2}-\frac {a}{2}-\frac {x^2}{2}-\frac {x}{2}}{x+1} \] ✓ Mathematica : cpu = 0.306655 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-a^2-2 a x-8 c_1 \log (x+1)+4 c_1^2-x^2+4 \log ^2(x+1)\right )\right \}\right \}\] ✓ Maple : cpu = 0.395 (sec), leaf count = 33
\[ \left \{ {\it \_C1}+{\frac {a}{2}}+2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]