71.4.4 problem 4

Internal problem ID [14305]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 4
Date solved : Monday, March 31, 2025 at 12:16:26 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=diff(y(x),x) = ln(-1+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (x +\operatorname {Ei}_{1}\left (-\textit {\_Z} \right )+c_1 \right )}+1 \]

✓ Mathematica. Time used: 0.181 (sec). Leaf size: 31

ode=D[y[x],x]==Log[y[x]-1]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\log (K[1]-1)}dK[1]\&\right ][x+c_1] \\ y(x)\to 2 \\ \end{align*}

✓ Sympy. Time used: 0.281 (sec). Leaf size: 8

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

\[ \operatorname {li}{\left (y{\left (x \right )} - 1 \right )} = C_{1} + x \]