\[ y'(x)=\frac {\sqrt {x^2+3 y(x)}-\frac {2 x^2}{3}-\frac {2 x}{3}}{x+1} \] ✓ Mathematica : cpu = 0.371279 (sec), leaf count = 37
\[\left \{\left \{y(x)\to \frac {1}{12} \left (-4 x^2+9 \log ^2(x+1)-18 c_1 \log (x+1)+9 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.372 (sec), leaf count = 23
\[\left \{c_{1}+\frac {3 \ln \left (x +1\right )}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0\right \}\]