60.1.444 problem 447

Internal problem ID [10458]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 447
Date solved : Monday, January 27, 2025 at 07:46:06 PM
CAS classification : [_quadrature]

\begin{align*} \left (x^{2}-1\right ) {y^{\prime }}^{2}-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 33

dsolve((x^2-1)*diff(y(x),x)^2-1 = 0,y(x), singsol=all)
 

\begin{align*} y &= \ln \left (x +\sqrt {x^{2}-1}\right )+c_{1} \\ y &= -\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)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\log \left (\sqrt {x^2-1}+x\right )+c_1 \\ y(x)\to \log \left (\sqrt {x^2-1}+x\right )+c_1 \\ \end{align*}