67.3.36 problem 4.7 (j)

Internal problem ID [16357]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.7 (j)
Date solved : Thursday, October 02, 2025 at 01:22:25 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 11

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

\[ y = \ln \left ({\mathrm e}^{x} c_1 -1\right ) \]

✓ Mathematica. Time used: 1.097 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \log \left (-1+e^{x+c_1}\right )\\ y(x)&\to -i \pi \\ y(x)&\to i \pi \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 10

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

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