Internal problem ID [7644]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y^{2}+1}{{| y+\sqrt {1+y}|} \left (x +1\right )^{\frac {3}{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
dsolve(diff(y(x),x) - (1+ y(x)^2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)^3)=0,y(x), singsol=all)
\[ -\frac {2}{\sqrt {x +1}}-\left (\int _{}^{y \relax (x )}\frac {{| \textit {\_a} +\sqrt {\textit {\_a} +1}|}}{\textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.477 (sec). Leaf size: 62
DSolve[y'[x] - (1+ y[x]^2)/(Abs[y[x]+Sqrt[1+y[x]]]*Sqrt[1+x]^3)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}