73.3.36 problem 4.7 (j)

Internal problem ID [15070]
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)
Date solved : Tuesday, January 28, 2025 at 07:29:36 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.124 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 1.223 (sec). Leaf size: 32

DSolve[D[y[x],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*}