\[ y'(x)-\frac {y(x)^2+1}{(x+1)^{3/2} \left | y(x)+\sqrt {y(x)+1}\right | }=0 \] ✓ Mathematica : cpu = 0.188141 (sec), leaf count = 48
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left | K[1]+\sqrt {K[1]+1}\right | }{K[1]^2+1}dK[1]\& \right ]\left [-\frac {2}{\sqrt {x+1}}+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 5.726 (sec), leaf count = 35
\[\left \{c_{1}-\left (\int _{}^{y \left (x \right )}\frac {{| \textit {\_a} +\sqrt {\textit {\_a} +1}|}}{\textit {\_a}^{2}+1}d \textit {\_a} \right )-\frac {2}{\sqrt {x +1}} = 0\right \}\]