63.1.5 problem 5

Internal problem ID [13029]
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 : Tuesday, January 28, 2025 at 04:49:41 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==Exp[-x[t]],x[t],t,IncludeSingularSolutions -> True]
 

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