67.6.9 problem 7.4 (g)

Internal problem ID [16435]
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 : Thursday, October 02, 2025 at 01:32:59 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

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

\[ y = -\ln \left (-\frac {x}{-1+x \,{\mathrm e}^{c_1}}\right )-c_1 \]

✓ Mathematica. Time used: 0.486 (sec). Leaf size: 25

ode=1+Exp[y[x]]+x*Exp[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*exp(y(x))*Derivative(y(x), x) + exp(y(x)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\frac {C_{1}}{x} - 1 \right )} \]