Internal problem ID [4972]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (1+z^{\prime }\right ) {\mathrm e}^{-z}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.03 (sec). Leaf size: 15
dsolve((1+diff(z(t),t))*exp(-z(t))=1,z(t), singsol=all)
\[ z \relax (t ) = \ln \left (-\frac {1}{c_{1} {\mathrm e}^{t}-1}\right ) \]
✓ Solution by Mathematica
Time used: 0.742 (sec). Leaf size: 21
DSolve[(1+z'[t])*Exp[-z[t]]==1,z[t],t,IncludeSingularSolutions -> True]
\begin{align*} z(t)\to \log \left (\frac {1}{1+e^{t+c_1}}\right ) \\ z(t)\to 0 \\ \end{align*}