71.8.1 problem 1

Internal problem ID [14364]
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 : Monday, March 31, 2025 at 12:19:31 PM
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*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 13

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

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

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

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

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

✓ Sympy. Time used: 0.133 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \log {\left (x - 1 \right )} + 1 - i \pi \]