\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/2\,{\frac {{x}^{3} \left ( \sqrt {a}x+\sqrt {a}-2\,\sqrt {a{x}^{4}+8\,y \left ( x \right ) } \right ) \sqrt {a}}{1+x}}=0} \]
Mathematica: cpu = 0.351044 (sec), leaf count = 128 \[ \left \{\left \{y(x)\to \frac {1}{72} \left (-96 a c_1 x^3+144 a c_1 x^2-288 a c_1 x+288 a c_1 \log (x+1)+144 a c_1^2-432 a c_1+16 a x^6-48 a x^5+123 a x^4-96 a x^3 \log (x+1)-72 a x^2+144 a x^2 \log (x+1)+432 a x+144 a \log ^2(x+1)-288 a x \log (x+1)-432 a \log (x+1)+324 a\right )\right \}\right \} \]
Maple: cpu = 0.437 (sec), leaf count = 41 \[ \left \{ {\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1 }{\sqrt {a}}}}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]