\[ y'(x)=\frac {\sqrt {x^2+3 y(x)}-\frac {2 x^2}{3}-\frac {2 x}{3}}{x+1} \] ✓ Mathematica : cpu = 0.284733 (sec), leaf count = 37
DSolve[Derivative[1][y][x] == ((-2*x)/3 - (2*x^2)/3 + Sqrt[x^2 + 3*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{12} \left (-4 x^2+9 \log ^2(x+1)-18 c_1 \log (x+1)+9 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.396 (sec), leaf count = 23
dsolve(diff(y(x),x) = -1/3*(2*x^2+2*x-3*(x^2+3*y(x))^(1/2))/(1+x),y(x))
\[c_{1}+\frac {3 \ln \left (1+x \right )}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0\]