59.1.2 problem 5.1 (ii)

Internal problem ID [14986]
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 : Thursday, October 02, 2025 at 09:58:06 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = -\operatorname {arctanh}\left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 26

ode=D[y[x],x]==1/(x^2-1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} (\log (1-x)-\log (x+1)+2 c_1) \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x**2 - 1),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (x - 1 \right )}}{2} - \frac {\log {\left (x + 1 \right )}}{2} \]