65.6.9 problem 9

Internal problem ID [15702]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:23:30 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.092 (sec). Leaf size: 15

ode:=x*exp(y(x))+diff(y(x),x) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \ln \left (2\right )-\ln \left (x^{2}+2\right ) \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 16

ode=x*Exp[y[x]]+D[y[x],x]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (2)-\log \left (x^2+2\right ) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \log {\left (\frac {1}{x^{2} + 2} \right )} + \log {\left (2 \right )} \]