\[ y'(x)=\frac {x \left (3 x^2 \sqrt {x^2+3 y(x)}-2 x-2\right )}{3 (x+1)} \] ✓ Mathematica : cpu = 0.343419 (sec), leaf count = 101
DSolve[Derivative[1][y][x] == (x*(-2 - 2*x + 3*x^2*Sqrt[x^2 + 3*y[x]]))/(3*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{48} \left (4 x^6-12 x^5+33 x^4-36 x^3-24 x^3 \log (x+1)-24 c_1 x^3+20 x^2+36 x^2 \log (x+1)+36 c_1 x^2+36 \log ^2(x+1)-72 x \log (x+1)-72 c_1 x+72 c_1 \log (x+1)+36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.504 (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))
\[c_{1}+\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 \ln \left (1+x \right )}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0\]