ODE No. 63

$$y^{\prime }(x)-\frac{y(x{)}^2+1}{(x+1{)}^{3/2}|y(x)+\sqrt{y(x)+1}|}=0$$ ✓ Mathematica : cpu = 0.145814 (sec), leaf count = 48

DSolve[-((1 + y[x]^2)/((1 + x)^(3/2)*Abs[y[x] + Sqrt[1 + y[x]]])) + Derivative[1][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{|K[1]+\sqrt{K[1]+1}|}{K[1{]}^2+1}dK[1]\mathrm{\&}][-\frac{2}{\sqrt{x+1}}+c_1]\}\right\}$$ ✓ Maple : cpu = 5.703 (sec), leaf count = 35

dsolve(diff(y(x),x)-(y(x)^2+1)/abs(y(x)+(1+y(x))^(1/2))/(1+x)^(3/2) = 0,y(x))
 

$$-\frac{2}{\sqrt{1+x}}-\left({\int }_{}^{y\left(x\right)}\frac{|\mathit{\text{\_a}}+\sqrt{\mathit{\text{\_a}}+1}|}{{\mathit{\text{\_a}}}^2+1}d\mathit{\text{\_a}}\right)+c_1=0$$