\[ y'(x)=-\frac {\sqrt {a} \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x^4+\sqrt {a} x^3\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.436083 (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 = 1.067 (sec), leaf count = 28
\[ \left \{ -{\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1}{\sqrt {a}}}}+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]