\[ y'(x)-\frac {y(x)^2+1}{(x+1)^{3/2} \left | y(x)+\sqrt {y(x)+1}\right | }=0 \] ✓ Mathematica : cpu = 0.118269 (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 = 5.646 (sec), leaf count = 35
\[ \left \{ -2\,{\frac {1}{\sqrt {1+x}}}-\int ^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{2}+1} \left | {\it \_a}+\sqrt {{\it \_a}+1} \right | }{d{\it \_a}}+{\it \_C1}=0 \right \} \]