\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/2\,{\frac {{x}^{2}+x+ax+a-2\,\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.337543 (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 = 0.281 (sec), leaf count = 33 \[ \left \{ {\it \_C1}+{\frac {a}{2}}+2\,\ln \left ( 1+x \right ) -\sqrt { {x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0 \right \} \]