65.1.2 problem 5.1 (ii)

Internal problem ID [13626]
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 : Wednesday, March 05, 2025 at 10:05:32 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.000 (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: 0.004 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.147 (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)
 

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