\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/2\,{\frac { \left ( \sqrt {a}{x}^{4}+\sqrt {a}{x}^{3}-2\,\sqrt {a{x}^{4}+8\,y \left ( x \right ) } \right ) \sqrt {a}}{1+x}}=0} \]
Mathematica: cpu = 0.272035 (sec), leaf count = 41 \[ \left \{\left \{y(x)\to \frac {1}{8} \left (-32 a c_1 \log (x+1)+16 a c_1^2-a x^4+16 a \log ^2(x+1)\right )\right \}\right \} \]
Maple: cpu = 0.343 (sec), leaf count = 28 \[ \left \{ -{\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac { 1}{\sqrt {a}}}}+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]