Internal problem ID [5725]
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]
\[ \boxed {\left (1+z^{\prime }\right ) {\mathrm e}^{-z}=1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve((1+diff(z(t),t))*exp(-z(t))=1,z(t), singsol=all)
\[ z \left (t \right ) = \ln \left (-\frac {1}{c_{1} {\mathrm e}^{t}-1}\right ) \]
✓ Solution by Mathematica
Time used: 0.722 (sec). Leaf size: 28
DSolve[(1+z'[t])*Exp[-z[t]]==1,z[t],t,IncludeSingularSolutions -> True]
\begin{align*} z(t)\to \log \left (\frac {1}{2} \left (1-\tanh \left (\frac {t+c_1}{2}\right )\right )\right ) z(t)\to 0 \end{align*}