Internal problem ID [13014]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.7 (j).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-{\mathrm e}^{-y}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)=exp(-y(x))+1,y(x), singsol=all)
\[ y = \ln \left (c_{1} {\mathrm e}^{x}-1\right ) \]
✓ Solution by Mathematica
Time used: 1.163 (sec). Leaf size: 32
DSolve[y'[x]==Exp[-y[x]]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-1+e^{x+c_1}\right ) y(x)\to -i \pi y(x)\to i \pi \end{align*}