7.7.21 problem 21

Internal problem ID [199]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 21
Date solved : Friday, February 07, 2025 at 08:07:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve((x^2-1)*diff(y(x),x)+(x-1)*y(x)=1,y(x), singsol=all)
 

\[ y = \frac {\ln \left (x -1\right )+c_1}{x +1} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 18

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

\[ y(x)\to \frac {\log (x-1)+c_1}{x+1} \]