\[ y'(x)=\frac {x^3 \sqrt {4 a x-y(x)^2}+2 a x+2 a}{(x+1) y(x)} \] ✓ Mathematica : cpu = 2.77013 (sec), leaf count = 217
\[\left \{\left \{y(x)\to -\frac {1}{6} \sqrt {144 a x-4 x^6+12 x^5-33 x^4+36 x^3-36 x^2+24 x^3 \log (x+1)-36 x^2 \log (x+1)-24 c_1 x^3+36 c_1 x^2-36 \log ^2(x+1)+72 x \log (x+1)-72 c_1 x+72 c_1 \log (x+1)-36 c_1{}^2}\right \},\left \{y(x)\to \frac {1}{6} \sqrt {144 a x-4 x^6+12 x^5-33 x^4+36 x^3-36 x^2+24 x^3 \log (x+1)-36 x^2 \log (x+1)-24 c_1 x^3+36 c_1 x^2-36 \log ^2(x+1)+72 x \log (x+1)-72 c_1 x+72 c_1 \log (x+1)-36 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.358 (sec), leaf count = 39
\[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]