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 : Monday, January 27, 2025 at 03:23:25 PM
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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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