80.1.7 problem 8(a)

Internal problem ID [21125]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 8(a)
Date solved : Thursday, October 02, 2025 at 07:09:25 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }+\frac {x}{t^{2}-1}&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 22

ode:=diff(x(t),t)+1/(t^2-1)*x(t) = 0; 
ic:=[x(-2) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -\frac {i \sqrt {3}\, \left (t +1\right )}{\sqrt {-t^{2}+1}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 30

ode=D[x[t],t]+1/(t^2-1)*x[t]==0; 
ic={x[-2]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\frac {i \sqrt {3} \sqrt {t+1}}{\sqrt {1-t}} \end{align*}

✓ Sympy. Time used: 0.152 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = \frac {i \sqrt {t + 1}}{2 \sqrt {t - 1}} \]