\[ y'(x)=\frac {x \left (3 x^2 \sqrt {x^2+3 y(x)}-2 x-2\right )}{3 (x+1)} \] ✓ Mathematica : cpu = 0.436977 (sec), leaf count = 47
DSolve[Derivative[1][y][x] == (x*(-2 - 2*x + 3*x^2*Sqrt[x^2 + 3*y[x]]))/(3*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{3} \left (-x^2+\frac {1}{16} \left (2 x^3-3 x^2+6 x+6 \log \left (\frac {1}{x+1}\right )-6 c_1\right ){}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.403 (sec), leaf count = 36
dsolve(diff(y(x),x) = 1/3*x*(-2*x-2+3*x^2*(x^2+3*y(x))^(1/2))/(1+x),y(x))
\[c_{1}+\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 \ln \left (1+x \right )}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0\]