2.63   ODE No. 63

\[ y'(x)-\frac {y(x)^2+1}{(x+1)^{3/2} \left | y(x)+\sqrt {y(x)+1}\right | }=0 \] Mathematica : cpu = 0.145814 (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 = 5.703 (sec), leaf count = 35


\[-\frac {2}{\sqrt {1+x}}-\left (\int _{}^{y \relax (x )}\frac {{| \textit {\_a} +\sqrt {\textit {\_a} +1}|}}{\textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1} = 0\]