30.6.1 problem 1

Internal problem ID [7536]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:44:57 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

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

\[ y = -\operatorname {LambertW}\left (c_1 +{\mathrm e}^{x}\right ) \]

✓ Mathematica. Time used: 60.095 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to -W\left (e^x+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.221 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = - W\left (C_{1} + e^{x}\right ) \]