73.6.9 problem 7.4 (g)

Internal problem ID [15148]
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)
Date solved : Tuesday, January 28, 2025 at 07:38:05 AM
CAS classification : [_separable]

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 22

dsolve(1+exp(y(x))+x*exp(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.793 (sec). Leaf size: 25

DSolve[1+Exp[y[x]]+x*Exp[y[x]]*D[y[x],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*}