90.1.12 problem 23

Internal problem ID [25036]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 23
Date solved : Thursday, October 02, 2025 at 11:47:41 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 2.47 (sec). Leaf size: 32

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

\begin{align*} y(t)&\to \log \left (\frac {1}{2} \left (-1+\tanh \left (\frac {t-c_1}{2}\right )\right )\right )\\ y(t)&\to i \pi \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 14

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

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