63.1.5 problem 5

Internal problem ID [12950]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page 10
Problem number : 5
Date solved : Wednesday, March 05, 2025 at 08:54:38 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 8

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

\[ x \left (t \right ) = \ln \left (t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.213 (sec). Leaf size: 10

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

\[ x(t)\to \log (t+c_1) \]

✓ Sympy. Time used: 0.154 (sec). Leaf size: 7

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

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