50.1.28 problem 3(d)

Internal problem ID [7800]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 3(d)
Date solved : Wednesday, March 05, 2025 at 05:06:17 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=0 \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 14

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

\[ y = -\operatorname {arctanh}\left (x \right )+\operatorname {arctanh}\left (\frac {1}{2}\right )-\frac {i \pi }{2} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} (\log (3-3 x)-\log (x+1)-i \pi ) \]

✓ Sympy. Time used: 0.170 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {\log {\left (x - 1 \right )}}{2} - \frac {\log {\left (x + 1 \right )}}{2} + \frac {\log {\left (3 \right )}}{2} \]