71.8.1 problem 1

Internal problem ID [14435]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:31:01 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

dsolve([diff(y(x),x)=1/(x-1),y(0) = 1],y(x), singsol=all)
 

\[ y = \ln \left (x -1\right )+1-i \pi \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

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

\[ y(x)\to \log (x-1)-i \pi +1 \]