\[ y'(x)=-\frac {\sqrt {a} x^3 \left (-2 \sqrt {a x^4+8 y(x)}+\sqrt {a} x+\sqrt {a}\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.502292 (sec), leaf count = 128
\[\left \{\left \{y(x)\to \frac {1}{72} \left (16 a x^6-48 a x^5+123 a x^4-72 a x^2-96 a x^3 \log (x+1)+144 a x^2 \log (x+1)-96 a c_1 x^3+144 a c_1 x^2+432 a x+144 a \log ^2(x+1)-288 a x \log (x+1)-432 a \log (x+1)-288 a c_1 x+288 a c_1 \log (x+1)+324 a+144 a c_1{}^2-432 a c_1\right )\right \}\right \}\] ✓ Maple : cpu = 1.187 (sec), leaf count = 41
\[ \left \{ {\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }{\frac {1}{\sqrt {a}}}}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]