Internal problem ID [8025]
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]
\[ \boxed {\left (x^{2}-1\right ) {y^{\prime }}^{2}-1=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 33
dsolve((x^2-1)*diff(y(x),x)^2-1 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y \left (x \right ) = -\ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 41
DSolve[-1 + (-1 + x^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ y(x)\to \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1 \\ \end{align*}