Internal problem ID [535]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+1-{\mathrm e}^{-y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(t),t) = -1+exp(-y(t)),y(t), singsol=all)
\[ y \relax (t ) = -t +\ln \left ({\mathrm e}^{t +c_{1}}-1\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.871 (sec). Leaf size: 21
DSolve[y'[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*}