Internal problem ID [5887]
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]
\[ \boxed {y \,{\mathrm e}^{x y}+x \,{\mathrm e}^{x y} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.026 (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*}