42.4.13 problem Problem 3.20

Internal problem ID [8841]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.20
Date solved : Tuesday, September 30, 2025 at 05:57:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

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

\[ y = \frac {c_1}{x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to \frac {c_1}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 5

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

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