Internal problem ID [8782]
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]
\[ \boxed {\left (x^{2}-1\right ) {y^{\prime }}^{2}=1} \]
✓ 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: 0.006 (sec). Leaf size: 89
DSolve[-1 + (-1 + x^2)*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) y(x)\to \frac {1}{2} \left (-\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1\right ) \end{align*}