10.4.4 problem 5

Internal problem ID [1185]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:43:20 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

dsolve(diff(y(t),t) = -1+exp(-y(t)),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.797 (sec). Leaf size: 21

DSolve[D[y[t],t] == -1+Exp[-y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \log \left (1+e^{-t+c_1}\right ) \\ y(t)\to 0 \\ \end{align*}