\[ y'(x)=\frac {x^3 \sqrt {4 a x-y(x)^2}+2 a x+2 a}{(x+1) y(x)} \] ✓ Mathematica : cpu = 5.48258 (sec), leaf count = 143
\[\left \{\left \{y(x)\to -\frac {1}{6} \sqrt {144 a x-\left (6 c_1+2 x^3-3 x^2+6 x\right ){}^2+12 \left (6 c_1+2 x^3-3 x^2+6 x\right ) \log (x+1)-36 \log ^2(x+1)}\right \},\left \{y(x)\to \frac {1}{6} \sqrt {144 a x-\left (6 c_1+2 x^3-3 x^2+6 x\right ){}^2+12 \left (6 c_1+2 x^3-3 x^2+6 x\right ) \log (x+1)-36 \log ^2(x+1)}\right \}\right \}\]
✓ Maple : cpu = 0.287 (sec), leaf count = 39
\[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]