\[ y'(x)=\frac {\sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a x}{2}-\frac {a}{2}-\frac {x^2}{2}-\frac {x}{2}}{x+1} \] ✓ Mathematica : cpu = 0.337539 (sec), leaf count = 44
\[\left \{\left \{y(x)\to -\frac {a^2}{4}-\frac {a x}{2}-2 c_1 \log (x+1)+c_1^2-\frac {x^2}{4}+\log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.414 (sec), leaf count = 33
\[ \left \{ {\it \_C1}+{\frac {a}{2}}+2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]