\[ y'(x)=-\frac {\sqrt {a} x^3 \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x+\sqrt {a}\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.341816 (sec), leaf count = 128
\[\left \{\left \{y(x)\to \frac {1}{72} \left (-96 a c_1 x^3+144 a c_1 x^2-288 a c_1 x+288 a c_1 \log (x+1)+144 a c_1^2-432 a c_1+16 a x^6-48 a x^5+123 a x^4-96 a x^3 \log (x+1)-72 a x^2+144 a x^2 \log (x+1)+432 a x+144 a \log ^2(x+1)-288 a x \log (x+1)-432 a \log (x+1)+324 a\right )\right \}\right \}\] ✓ Maple : cpu = 0.672 (sec), leaf count = 41
\[ \left \{ {\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1}{\sqrt {a}}}}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]