90.5.25 problem 26

Internal problem ID [25144]
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 71
Problem number : 26
Date solved : Thursday, October 02, 2025 at 11:54:38 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

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

\[ y = -\ln \left (c_1 +t \right ) \]

✓ Mathematica. Time used: 0.127 (sec). Leaf size: 14

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

\begin{align*} y(t)&\to -\log (t-c_1) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 8

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

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