7.7.17 problem 17

Internal problem ID [195]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 17
Date solved : Friday, February 07, 2025 at 08:04:25 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 15

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

\[ {\mathrm e}^{x y}+{\mathrm e}^{x}+{\mathrm e}^{y}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 20

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

\[ \text {Solve}\left [e^{y(x)}+e^{x y(x)}+e^x=c_1,y(x)\right ] \]