65.1.2 problem 5.1 (ii)

Internal problem ID [13705]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.1 (ii)
Date solved : Tuesday, January 28, 2025 at 05:55:41 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-1} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 10

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

\[ y = -\operatorname {arctanh}\left (x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[D[y[x],x]==1/(x^2-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {1}{K[1]^2-1}dK[1]+c_1 \]