Internal problem ID [8027]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 447.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) \left (y^{\prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.19 (sec). Leaf size: 33
dsolve((x^2-1)*diff(y(x),x)^2-1 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y \relax (x ) = -\ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 41
DSolve[-1 + (-1 + x^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ y(x)\to \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ \end{align*}