\[ y'(x)=\frac {x^2 \left (2 x \sqrt {x^3-6 y(x)}+x+1\right )}{2 (x+1)} \] ✓ Mathematica : cpu = 0.226 (sec), leaf count = 90
\[\left \{\left \{y(x)\to \left (-3 c_1+x^3-\frac {3 x^2}{2}+3 x\right ) \log (x+1)+\frac {1}{24} \left (8 \left (3 c_1+5\right ) x^3-36 \left (c_1+1\right ) x^2+72 c_1 x-36 c_1^2-4 x^6+12 x^5-33 x^4\right )-\frac {3}{2} \log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.277 (sec), leaf count = 37
\[ \left \{ {\it \_C1}-{x}^{3}+{\frac {3\,{x}^{2}}{2}}-3\,x+3\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt {{x}^{3}-6\,y \left ( x \right ) }=0 \right \} \]