\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,ax+2\,a+{x}^{3}\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}}{ \left ( 1+x \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 5.563707 (sec), leaf count = 217 \[ \left \{\left \{y(x)\to -\frac {1}{6} \sqrt {144 a x-24 c_1 x^3+36 c_1 x^2-72 c_1 x+72 c_1 \log (x+1)-36 c_1^2-4 x^6+12 x^5-33 x^4+36 x^3+24 x^3 \log (x+1)-36 x^2-36 x^2 \log (x+1)-36 \log ^2(x+1)+72 x \log (x+1)}\right \},\left \{y(x)\to \frac {1}{6} \sqrt {144 a x-24 c_1 x^3+36 c_1 x^2-72 c_1 x+72 c_1 \log (x+1)-36 c_1^2-4 x^6+12 x^5-33 x^4+36 x^3+24 x^3 \log (x+1)-36 x^2-36 x^2 \log (x+1)-36 \log ^2(x+1)+72 x \log (x+1)}\right \}\right \} \]
Maple: cpu = 0.203 (sec), leaf count = 39 \[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{ \frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{ \it \_C1}=0 \right \} \]