\[ y'(x)=-\frac {\sqrt {a} \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x^4+\sqrt {a} x^3\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.532765 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-a x^4+16 a \log ^2(x+1)-32 a c_1 \log (x+1)+16 a c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.694 (sec), leaf count = 28
\[\left \{-c_{1}+\ln \left (x +1\right )-\frac {\sqrt {a \,x^{4}+8 y \left (x \right )}}{4 \sqrt {a}} = 0\right \}\]