\[ y'(x)-x (x+2) y(x)^3-(x+3) y(x)^2=0 \] ✓ Mathematica : cpu = 1.05756 (sec), leaf count = 485
\[\text {Solve}\left [c_1=-\frac {\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (\frac {\sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}-\cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {i \sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}}{\frac {i \sqrt {\frac {2}{\pi }} \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}} \left (i \sinh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )-\frac {i \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}-\frac {\sqrt {\frac {2}{\pi }} \left (\frac {x+1}{2}+\frac {1}{2}\right ) \cosh \left (\sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}\right )}{\sqrt {-i \sqrt {\frac {1}{2 y(x)}+\frac {1}{4} (x+1)^2-\frac {1}{4}}}}},y(x)\right ]\] ✓ Maple : cpu = 0.023 (sec), leaf count = 40
\[c_{1}+\arctanh \left (\frac {\sqrt {y \relax (x )}\, x}{\sqrt {x \left (x +2\right ) y \relax (x )+2}}\right )+\frac {\sqrt {x \left (x +2\right ) y \relax (x )+2}}{2 \sqrt {y \relax (x )}} = 0\]