Internal problem ID [13412]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.4 (g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(1+exp(y(x))+x*exp(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (-\frac {x}{x \,{\mathrm e}^{c_{1}}-1}\right )-c_{1} \]
✓ Solution by Mathematica
Time used: 0.745 (sec). Leaf size: 25
DSolve[1+Exp[y[x]]+x*Exp[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-1+\frac {e^{c_1}}{x}\right ) \\ y(x)\to i \pi \\ \end{align*}