48.4.13 problem Problem 3.20

Internal problem ID [7555]
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 : Monday, January 27, 2025 at 03:05:44 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\[ y = \frac {c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 16

DSolve[y[x]*Exp[x*y[x]]+x*Exp[x*y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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