3.63   ODE No. 63

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\frac{{\left(y\left(x\right)\right)}^2+1}{|y\left(x\right)+\sqrt{1+y\left(x\right)}|{(1+x)}^{3/2}}=0}}$$

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

Mathematica: cpu = 558.947977 (sec), leaf count = 47 $$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{|K[1]+\sqrt{K[1]+1}|}{K[1{]}^2+1}dK[1]\mathrm{\&}][c_1-\frac{2}{\sqrt{x+1}}]\}\right\}$$

Maple: cpu = 0.094 (sec), leaf count = 35 $$\{-2\frac{1}{\sqrt{1+x}}-{\int }^{y\left(x\right)}\frac{1}{{\mathit{\_}\mathit{a}}^2+1}|\mathit{\_}\mathit{a}+\sqrt{\mathit{\_}\mathit{a}+1}|d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$