\[ y'(x)=-\frac {\sqrt {a} x^3 \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x+\sqrt {a}\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.343122 (sec), leaf count = 96
\[\left \{\left \{y(x)\to \frac {1}{72} a \left (-96 c_1 x^3+72 \left (2 c_1-1\right ) x^2-48 \left (-6 c_1+2 x^3-3 x^2+6 x+9\right ) \log (x+1)-144 \left (2 c_1-3\right ) x+36 \left (3-2 c_1\right ){}^2+16 x^6-48 x^5+123 x^4+144 \log ^2(x+1)\right )\right \}\right \}\]
✓ Maple : cpu = 0.693 (sec), leaf count = 41
\[ \left \{ {\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1}{\sqrt {a}}}}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]