\[ y'(x)=\frac {x^2 \left (2 x \sqrt {x^3-6 y(x)}+x+1\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.288318 (sec), leaf count = 101
\[\left \{\left \{y(x)\to \frac {1}{24} \left (-4 x^6+12 x^5-33 x^4+40 x^3-36 x^2+24 x^3 \log (x+1)-36 x^2 \log (x+1)+24 c_1 x^3-36 c_1 x^2-36 \log ^2(x+1)+72 x \log (x+1)+72 c_1 x-72 c_1 \log (x+1)-36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.656 (sec), leaf count = 37
\[ \left \{ {\it \_C1}-{x}^{3}+{\frac {3\,{x}^{2}}{2}}-3\,x+3\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt {{x}^{3}-6\,y \left ( x \right ) }=0 \right \} \]