\[ y'(x)=\frac {\sqrt {x^3-6 y(x)}+\frac {x^3}{2}+\frac {x^2}{2}}{x+1} \] ✓ Mathematica : cpu = 0.287367 (sec), leaf count = 35
DSolve[Derivative[1][y][x] == (x^2/2 + x^3/2 + Sqrt[x^3 - 6*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{6} \left (x^3-9 \log ^2(x+1)+18 c_1 \log (x+1)-9 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.4 (sec), leaf count = 23
dsolve(diff(y(x),x) = 1/2*(x^3+x^2+2*(x^3-6*y(x))^(1/2))/(1+x),y(x))
\[c_{1}-3 \ln \left (1+x \right )-\sqrt {x^{3}-6 y \left (x \right )} = 0\]