80.5.5 problem 7

Internal problem ID [18563]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 32. Problems at page 89
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:00:12 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 33

dsolve((x^2-1)*diff(y(x),x)^2=1,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: 0.004 (sec). Leaf size: 41

DSolve[(x^2-1)*D[y[x],x]^2==1,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*}