4.13 problem Problem 3.20

Internal problem ID [5134]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.016 (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)
 

\[ y \relax (x ) = \frac {c_{1}}{x} \]

Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 16

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

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