2.63   ODE No. 63

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)-\frac{y(x{)}^2+1}{(x+1{)}^{3/2}|y(x)+\sqrt{y(x)+1}|}=0$$ ✓ Mathematica : cpu = 0.118269 (sec), leaf count = 48

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{|K[1]+\sqrt{K[1]+1}|}{K[1{]}^2+1}dK[1]\mathrm{\&}][-\frac{2}{\sqrt{x+1}}+c_1]\}\right\}$$ ✓ Maple : cpu = 5.646 (sec), leaf count = 35

$$\{-2\frac{1}{\sqrt{1+x}}-{\int }^{y\left(x\right)}\frac{1}{{\mathit{\_}\mathit{a}}^2+1}|\mathit{\_}\mathit{a}+\sqrt{\mathit{\_}\mathit{a}+1}|d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$