65.5.5 problem 5

Internal problem ID [15688]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:23:11 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 10

ode:=diff(y(x),x) = 1/(x-1); 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to \log (x-1)+1 \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 8

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

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