88.1.3 problem 17

Internal problem ID [23946]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:46:43 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 17

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

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