\[ y'(x)=-\frac {\sqrt {a} \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x^4+\sqrt {a} x^3\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.235641 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -4 a c_1 \log (x+1)+2 a c_1^2-\frac {a x^4}{8}+2 a \log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.52 (sec), leaf count = 28
\[ \left \{ -{\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1}{\sqrt {a}}}}+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]